| LI BRARY OF CONGRESS. V 
I *Lf. QB45 \\ 



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'UNITED STATES OF AMKHICA.! 



m 



1. Great Cluster of Stars in Hercules. 
2. Whirlpool Nebula of Lord Rosse. 




SHELL'S OLMSTED'S SCHOOL ASTRONOMY. 

COMPENDIUM 



OF 



ASTEONOMT: 

gJbajjfeb to % $se of 

SCHOOLS AND ACADEMIES. 



BY 

DENISON* OLMSTED, LL.D., 

LATE PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE. 

KEVISED BY 

E, S. SNELL, LL.D., 

PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY IN AMHERST COLLEGE. 



C NEW YOEK : 
COLLINS & BBOTHEB, 

No. 106 LEONARD STREET. 



1868. 
V 



Entered, according to Act of Congress, in the year 1S67, by 
JULIA M. OLMSTED, 

FOE THE CHILDREN OF DENISON OLMSTED, DECEASED, 

In the Clerk's Office of the District Court of the United States for the District of 
Connecticut. 





Electrotyped by Smith & McDougal, 82 and 84 Beekman St., N. Y. 



O" 



PEEFACB 



I have endeavored, in the present volume, to per- 
form a work for Professor Olmsted's School Astron- 
omy, similar to that which I performed a few years 
since for his School Philosophy. Besides bringing 
the science more fully down to the present time, I 
have made it my special aim to present the facts and 
principles of the subject in clear language, and in 
few words, believing such a style most profitable to 
the pupil and most satisfactory to the teacher. It 
is believed that a decided improvement will be 
found in the engravings. Those which in former 
editions were erroneous have given place to more 
correct ones, taken from the revised College As- 
tronomy, and a large proportion of the remain- 
der have been changed in their style, and newly 
drawn and engraved expressly for this edition. 

E. S. SNELL. 

Amherst College, October, 1867. 



CONTENTS 



CHAPTER I. 

GENERAL FORM AND DIMENSION'S OF THE EARTH — THE 
DIURNAL MOTION — ARTIFICIAL GLOBES. 



PAGE 

Astronomy 13 

Form of the earth 14 

Proofs that it is globular 14 

The words up and down 15 

Size of the earth 16 

Inequalities of surface 16 

The diurnal rotation IT 

The equator of the earth 17 

Meridians ._ 17 

Latitude and longitude 17 

The terrestrial sphere 18 

The celestial sphere 18 

The horizon 18 

The vertical circles 19 

Altitude and azimuth 19 

Celestial equator 19 



PAGE 

The ecliptic 21 

Equinoxes 21 

Solstices 21 

The colures 21 

Signs of the ecliptic 22 

Right ascension and declination 22 

Celestial longitude and latitude 22 

Apparent daily motion of the heavens 23 

Rising, setting, culmination 23 

Diurnal circles and horizon 24 

The right sphere 25 

The parallel sphere 26 

The oblique sphere 26 

Artificial globes 27 

Problems on the terrestrial globe 29 

Problems on the celestial globe 30 



CHAPTER II. 

PARALLAX — ATMOSPHERIC REFRACTION TWILIGHT. 



Parallax 38 

Diurnal parallax 33 

Greatest at the horizon 35 

Diminishes as distance increases 35 

Horizontal parallax 35 

Parallax of the moon 35 



Atmospheric refraction 35 

Its effect on rising and setting 36 

Distortion of the sun's disk 37 

Illumination of the sky 37 

Twilight 38 

Duration of twilight 39 



CHAPTER IH. 



ASTRONOMICAL INSTRUMENTS — THE EARTH S MOTION ABOUT 
THE SUN — THE SEASONS FORM OF THE EARTH'S ORBIT. 



The equatorial telescope 40 

The transit instrument 40 

The astronomical clock 42 

Sidereal time .- 42 

To find right ascension 42 

To find declination 42 



The mural circle 43 

The altitude and azimuth instru- 
ment 43 

The sextant 44 

Observations of the sun's place 45 

The ecliptic and zodiac 46 



Vlll 



CONTENTS 



PAGE 

The tropics and polar circles 46 

Terrestrial zones 47 

The annual motion observed without 

instruments 4S 

A motion of the earth, not the sun.. . 48 

Cause of the change of seasons 49 

Causes of heat in summer and of cold 

in winter 51 



PAGE 

Time of greatest heat and greatest cold 52 

Effect of no obliquity on seasons 52 

Obliquity of 90° 53 

To find the form of the earth's orbit. . 53 

Perihelion, aphelion, etc 54 

Line of apsides 55 

Effect of sun's distance on the sea- 
sons 55 



CHAPTER IV. 



SIDEREAL TIME — MEAN AND APPARENT SOLAR TIME THE 

CALENDAR. 



The sidereal day 57 

The mean solar day 57 

The apparent solar day 53 

Causes of unequal solar days 58 

The equation of time 59 



Civil and astronomical timer 59 

The Julian calendar 60 

The Gregorian calendar 60 

Days of the month and of the week... . 61 



CHAPTER V. 



OBLATE FORM OF THE EARTH ITS MASS AND DENSITY 

PROOFS OF ITS ROTATION ON AN AXIS. 



Central forces 63 

Illustrations 63 

Loss of weight on the earth 64 

Loss from a second cause 64 



Oblate form of the earth 64 

Equatorial belt 65 

Weight and density of the earth. ..... 67 

Proofs of the earth's rotation 67 



CHAPTER VI. 



THE SUN — SOLAR SPOTS — CONDITION OF THE SUN'S SUR- 
FACE — THE ZODIACAL LIGHT. 



The form of the sun 69 

The sun's distance and size 69 

The sun's mass and strength of gravity 70 

Diurnal rotation of the sun 70 

Its apparent time 71 

Its real time 71 



Appearance of solar spots 71 

Their motions and changes 72 

Their nature 73 

Herschel's theory 73 

The zodiacal light 73 



CHAPTER VII. 



GRAVITATION — KEPLER S LAWS MOTION IN AN ELLIPTICAL 

ORBIT — PRECESSION OF THE EQUINOXES. 



Gravitation . . : 75 

First law of gravitation 75 

Second law 76 

Kepler's laws 76 

The first law 76 

The second law 77 

The third law 78 

Paths of projectiles 7S 

Effect of increased velocity 78 



Why a planet returns from aphelion . . 79 
Why a planet departs from aphelion.. 80 

Precession of equinoxes 81 

Signs of ecliptic displaced 81 

Motion of the poles 82 

Cause of precession 82 

The tropical year 83 

The sidereal year 83 



C ONTENTS. 



IX 



CHAPTER VIII. 



THE MOON ITS EEVOLUTIONS — ITS PHASES THE CONDITION 

OF ITS SUEFACE. 



PAGE 

Distance and size of the moon 84 

Eevolution about the earth 84 

Months 85 

Nodes t 85 

Conj unction and opposition 85 

Quadratures 86 

Octants 86 

Form of orbit 86 

Diurnal motion 86 

Libration of longitude 87 

Libration of latitude 87 

Diurnal libration 87 

Eevolution round the sun 88 

Phases of the moon 88 



PAGE 

Moon running high or low 90 

The harvest moon 90 

Inequalities of moon's surface 91 

Form of valleys 92 

Volcanic appearance 92 

Height of its mountains 93 

No atmosphere or vapor 93 

Changes of temperature on the moon. 94 

View of the earth from the moon 94 

As to magnitude 94 

As to phase 94 

As to position in the sky 95 

As to surface 95 



CHAPTER IX. 



ECLIPSES OF THE MOON AND SUN. 



General relations in eclipses 97 

Eclipse months 98 

Eclipse of the moon 99 

Forms of shadows 99 

Duration of eclipse 100 

Appearance of moon 100 

Eclipse of the sun 100 

Total shadow and penumbra of the 
moon 101 



Total and partial eclipses of the sun . 101 

Annular eclipse 103 

Velocity of the shadow 103 

Eelative number of solar and lunar 

eclipses 103 

Eclipses at the moon 104 

True form of shadows 104 



CHAPTER X. 



LONGITUDE — TIDES. 



Local time 105 

Connection between longitude and 

local time 105 

Longitude by the chronometer 106 

Longitude by a lunar eclipse 106 

By eclipses of Jupiter's satellites 106 

By a solar eclipse 107 

By occupations of stars 107 

By the lunar method 107 

By the magnetic telegraph 108 

Change of days in going round the 

earth 109 

Ambiguity as to days among the 
islands of the Pacific . >. 109 



Tides, high and low water 110 

Spring and neap tides Ill 

Opposite tides Ill 

Form of the water acted on by the 

moon Ill 

Direct and opposite tides 112 

Tides by the sun 112 

Joint action of sun and moon 113 

Effect of inertia of water 113 

Diurnal inequality 114 

Effects of coasts 115 

Cotidal lines 116 

Tides in lakes 118 



CONTENTS. 



CHAPTER XL 

THE PLANETS — TABULAR STATEMENTS — MERCURY — VENUS 
— MARS. 



PAGE 

Planetary bodies classified 119 

Three groups 119 

Inferior planets 120 

Superior planets 120 

Satellites 120 

Table of distances 121 

Table of revolutions 121 

Table of magnitudes 122 

Table of masses 122 

Sun and planets compared 123 

Diameters and distances compared. . 123 

Direction of motions 123 

Mercury — apparent motions 124 

Modified by the earth's motions 125 

Stationary points 127 



PAGE 

Form and position of Mercury's orbit 127 

Phases of Mercury 127 

Point of greatest brightness 128 

Transits of Mercury 12S 

Venus— its apparent motions 129 

The phases and brightness of Venus. 129 

Transits of Venus 129 

Use made of them 130 

Mars— its situation in the System... 130 

Apparent motions 130 

Phases and changes of apparent size. 132 

Appearance of disk 132 

Orbit and equator of Mars 133 

Days on the small planets , 133 



CHAPTER XII. 

THE PLANETOIDS JUPITER SATURN URANUS NEPTUNE 

DISTURBANCES OF THE PLANETS. 



Space between Mars and Jupiter 134 

The planetoids 134 

When discovered — number 134 

Characteristics 134 

Jupiter — its magnitude 136 

Its place in the System 136 

Its form and orbit 136 

Belts of Jupiter 137 

Satellites of Jupiter 138 

Eclipses of Jupiter and its satellites. 138 

Saturn— its disk 140 

Rings of Saturn 140 



Disappearance of rings 140 

Phenomena of rings at the planet. . . 142 

Satellites of Saturn 143 

Uranus — discovery 143 

Place in the System 143 

Satellites of Uranus 144 

Neptune — its discovery 144 

Motions of the planets disturbed 145 

Nodes retrograde . 146 

Apsides advance 146 

Eccentricity changes 146 

Stability preserved 146 



CHAPTER XIII. 



COMETS — SHOOTING STARS. 



Nucleus, coma, and envelope of a 

comet 148 

Number of comets 148 

Eccentricity of orbit 149 

Form and direction of tail 149 

Dimensions of comets 150 

Light of comets 151 

Mass of the comets 151 

Directions of their motions 152 

To find a comet's orbit 152 

Comets of known period 153 

Halley's comet 153 



Remarkable comets 15*3 

Comet of 1680 153 

Of 1744 153 

Of 1770 154 

Of 1843 154 

Of 1858 154 

Of 1861 154 

Shooting stars 155 

Gaseous meteors 155 

Solid meteors 156 

Aerolites 156 



CONTENTS 



XI 



CHAPTER XIV. 



THE FIXED STARS— CONSTELLATIONS. 



PAGE 

The stellar universe 158 

The fixed stars and their magnitudes 158 
Number included in the several mag- 
nitudes 159 

Cause of unequal brightness 159 

Constellations 160 

Star catalogues 161 

Descriptions of constellations 161 

Constellations of the Zodiac described 161 
Aries — Taurus — Gemini — Cancer — 

Leo— Virgo— Libra 161-165 

Scorpio — Sagittarius 165 

Capricorn us— Aquarius— Pisces 166 

Constellations north of the Zodiac. . . 168 

Ursa Minor — Ursa Major 168 

Draco — Cepheus — Cassiopeia — Cam- 
elopardalus 168-171 



PAGE 

Andromeda — Perseus 1T2 

Auriga — Leo Minor — Canes Venatici 

— Coma Berenices— Bootes 173 

Corona Borealis — Hercules — Lyra. . . 174 

Cygnus — Vulpecula 175 

Aquila — Antinous 176 

Delphinus— Pegasus 176, 177 

Ophiuchus 177 

Constellations south of the Zodiac. . . 177 

Cetus — Orion 177 

Lepus — Canis Major — Canis Minor. . 178 

Monoceros— Hydra 180 

Evening constellations of autumn.. . 181 

Of winter 182 

Of spring 183 

Of summer 183 



CHAPTER XV. 



Effect of telescopic power on fixed 

stars 185 

Annual parallax 185 

Distances of the stars 186 

Nature of the fixed stars 187 

Double stars 188 

Two ways of appearing double 188 

Binary stars 189 



Their periods 190 

Dimensions of their orbits 190 

Triple and quadruple stars 191 

Periodic and temporary stars 191 

Clusters of stars 192 

Nebulae 192 

Several forms 193 

The galaxy. 193 



COMPENDIUM OF ASTRONOMY, 



CHAPTEE I. 



GENEEAL FOEM AND DIMENSIONS OF THE EAETH — THE 
DIUENAL MOTION — AETTFICIAL GLOBES. 

1, General Definitions. — Astronomy is the science 
which treats of the heavenly bodies ; that is, of the 
sun, the planets and their satellites, the comets, and 
the fixed stars. 

The sun, planets, satellites and comets constitute 
the Solar System, which is so called because the sun 
is the principal body belonging to it, and controls the 
movements of all the others. 

The Fixed Stars are at an immense distance out- 
side of the solar system ; and each fixed star is sup- 
posed to be the sun of a separate system. Nearly 
all the bright points seen in the sky in a clear night 
are fixed stars, the whole number of which has never 
yet been counted. 



1. Define astronomy. What is the solar system ? What bodies 
are outside of the' solar system? 



14 THE EARTH. 

2. The Globular Form of the Earth, — The earth 
on which we live is one of the planets of the solar 
system. Its form, like that of all the other planets, 
is almost perfectly spherical. This is learned in sev- 
eral ways. 

1. When the sun casts the shadow of the earth on 
the moon in a lunar eclipse, the edge of the shadow 
is always circular. 

2. The earth shows its globular form by concealing 
the lower parts of objects when seen at a distance. 

Fig. 1. 




Thus, a person at A (Fig. 1) can see only the top of 
the mast of a ship, because the earth conceals all 
tne lower parts. If the surface of the ocean were 
perfectly flat, as in Fig. 2, then the whole ship could 
be seen, the lower part as well the upper, at any 
distance. 



2. To what class of bodies does the earth belong ? Mention the 
first proof that it is spherical— the second — the third. 



WORDS "up" and "down." 15 



Fig. 2. 




3. The measurements made on various parts of the 
earth lead to the conclusion that the distance from 
the surface to the center is everywhere about the 
same. 

3, Use of the words "up" and "dotvn." — "Wher- 
ever a person stands, up means from the earth, 
toward the highest point of the sky, and down means 
toward the center of the earth. Now, as the earth is 
a globe, the word up must express different directions 
in different places, though to us it always seems to be 
the same ; and so of the word dotvn, For example, 
the person at A (Fig. 3), sees the point E directly over 
his head, and calls that direction up; while at B, up 
is toward F, although directed 90° from AE. At 0, 
wp is toward G, precisely opposite to what it is at A. 



3. Explain the meaning of up, and of dovm. How can up be in 
different directions ? 



16 



THE EAETH 
Fig. 3. 




In like manner, down, which is everywhere toward the 
center, is in all possible directions from the different 
places on the earth. 

4, Size of the Earth. — If a person sails away from 
land till the ocean just conceals the whole height 
of a certain mountain, then, by means of its height 
and his distance from it, the Size of the earth can be 
easily calculated. For it is plain that the larger a 
globe is, the more nearly flat is its surface, and the 
farther off can the mountain be seen. In this and in 
other ways it is found that the diameter of the earth 
is 7,912 miles. Therefore the distance from the sur- 
face of the earth to its center is 3,956 miles, and the 
circumference is 24,857 miles. 

&. Inequalities of Surface. — As the surface of the 
earth is very uneven, and there are high mountains 



4. How can the size of the earth be found ? 
ter ? its radius ? its circumference ? 



What is its diame- 



EQUATOR AND ITS SECONDARIES. 17 

and deep valleys on many parts of it, it seems, at 
first, as though it could not have the regular form of 
a sphere. But we call an orange round, though it is 
covered with roughnesses ; and the mountains of the 
earth are comparatively a great deal smaller than the 
roughnesses on the outside of an orange. 

6. The Diurnal notation. — The earth revolves 
continually from west to east on an imaginary line 
drawn through its center. This line is called the 
Earth's Axis. The ends of the axis are called the 
North and South Poles of the earth. The time occu- 
pied by the earth in revolving once round is called 
a Day ; and this is divided into 24 hours. 

7» Tlie Earth's Equator and its Secondaries, — A 

great circle drawn round the earth, midway between 
its poles, is called the Equator. Meridians are great 
circles of the earth drawn through the poles, and 
therefore perpendicular to the equator. Since all 
great circles of a sphere which are perpendicular to 
a given great circle are called its Secondaries, there- 
fore the meridians are secondaries of the equator. 

The Latitude of a place is its distance north or south 
from the equator, measured on the meridian of that 
place, in degrees, minutes, and seconds. Parallels of 
latitude are small circles of the earth, parallel to the 
equator. 

5. How can the earth be spherical, when there are high moun- 
tains and deep valleys upon it ? 

6. Describe the earth's rotation. Define its axis — poles — a day. 

7. Define the equator and the meridians. What are the secon- 
daries of a great circle ? Meridians are secondaries of what ? De- 
fine latitude — longitude. How is a place on the earth determined ? 



18 THE EARTH. 

The Longitude of a place is the distance of its me- 
ridian, in degrees, minutes, and seconds, east or west 
from some standard meridian, as that of Greenwich, 
near London, or that of Washington. The situation 
of any place on the earth is determined by giving its 
latitude and longitude. 

8. The earth is called the Terrestrial Sphere. The 
Celestial Sphere is that apparent vault, called the 
Sky, which surrounds the earth on every side> and to 
which the heavenly bodies seem to be attached. The 
-celestial sphere is often called The Heavens. For most 
purposes of astronomy, the eye of an observer may 
be considered as the center of the celestial sphere. 

0* TJie Horizon and Ms Secondaries. — If the 

plumb-line (usually called the vertical), at any place 
on the earth, is supposed to be extended till it 
reaches the celestial sphere, it marks the Zenith above, 
and the Nadir below. And a plane passed through 
the center of the earth, perpendicular to the vertical, 
is called the Rational Horizon of that place. This is 
a great circle of the celestial sphere, and divides it 
into upper and lower hemispheres. The Sensible Hori- 
zon is parallel to the rational horizon, and passes 
through the place on the earth's surface. The planes 
of these two horizons are, therefore, nearly 4,000 
miles apart ; but so great is the distance of the heav- 



8. Describe the two spheres. What may be taken for the center 
of the celestial sphere ? 

9. Define zenith — nadir. Define the rational horizon — the sensi- 
ble horizon. Why are they one in the sky ? What are the secon- 



THE CELESTIAL EQUATOR. 19 

enly bodies, that the two planes seem to unite in the 
same great circle of the celestial sphere. 

The secondaries of the horizon intersect each other 
in the vertical line, and are called Vertical Circles. 
One of them is the meridian of the place. This cuts 
the horizon in the North and South Points of compass. 
The vertical circle, at right angles to the meridian, is 
called the Prime Vertical This cuts the horizon in 
the points called East and West 

The Altitude of a heavenly body is its elevation 
above the horizon, measured on the vertical circle 
passing through the body. The Zenith Distance of a 
body is the distance between it and the zenith, and 
is, therefore, the complement of its altitude. 

The Azimuth of a heavenly body is an arc of the 
horizon, measured from the meridian to the vertical 
circle, which passes through the body. The Ampli- 
tude is measured from the . vertical circle passing 
through the body to the prime vertical, and is, there- 
fore, the complement of the azimuth. The altitude, 
or zenith distance of a heavenly body, along with its 
azimuth or amplitude, determines its place in the vis- 
ible heavens. « 

10, The Celestial Equator and its Secondaries, 

If the axis on which the earth revolves is produced 
to the heavens, it becomes the Axis of the Celestial 
Sphere, and marks the North and South Poles of that 
sphere. The north pole is at present in the constel- 
lation of Ursa Minor. If the plane of the equator 
be extended in like manner, it becomes the Celestial 



daries of the horizon ? How are the points of compass fixed 
Define altitude — zenith distance — azimuth — amplitude. 



20 



THE EAETH 



Equator. The secondaries to this circle are called 
meridians, as on the earth. They are also called 
Hour-circles, because the arcs of the equator inter- 
cepted between them are used as measures of time. 




Tii 



Let n (Fig. 4) represent the north pole of the earth, 
s its south pole, eq the equator (projected in a straight 
line), o a given place whose north latitude is eo. 
Then N, S, are the poles of the celestial sphere, EQ 
is the celestial equator, Z is the zenith of the place o, 
E is its nadir, and HO its rational horizon ; oesqn 
is the terrestrial meridian of the same place, and 
ZESQN is its celestial meridian, or hour-circle. 



10. How are the celestial poles fixed? the celestial equator? 
What are the hour-circles ? Describe by the figure. 



THE ECLIPTIC. 21 

11. The Ecliptic. — Besides tlie equator, there is' 
an important circle of the celestial sphere, called the 
Ecliptic. It is that in which the sun appears to make 
its annual circuit around the heavens. It is inclined 
to the equator at an angle of nearly 23J°, crossing it 
in two opposite points, called the Equinoctial Points, 
or Equinoxes. The word " equinoxes" is used, also, to 
express the times at which the sun crosses the equa- 
tor, because at those times the nights are equal to the 
days. The vernal equinox is the time when the sun 
passes the equator from south to north, as it occurs 
in the spring, about March 21st. The autumnal equi- 
nox occurs on or near September 22d, when the sun 
returns to the south of the equator. 

The Solstitial Points, or Solstices, are those points of 
the ecliptic which are furthest north or south from 
the equator, situated, therefore, midway between the 
equinoxes. They are so named because there the 
sun stops in his advance northward or southward, and 
begins to return. The summer solstice is the point 
ivhere, and also the time w hen, the sun is furthest 
north, about the 22d of June. He passes the winter 
solstice on or near the 22d of December. 

The Equinoctial Colure is that secondary to the 
equator which passes through the equinoxes. The 
Solstitial Colure is that which passes through the sol- 
stices. They are, therefore, at right angles to each 
other, and the latter is a secondary to the ecliptic, as 
well as to the equator. 



11. Define the ecliptic — the equinoxes — and give their names. 
Define the solstices. When does the sun pass each of these four 
points ? Define the two colures. 



22 



THE EARTH. 



12. Signs of the Ecliptic. — The ecliptic is divided 
into 12 equal parts of 30° each, called Signs, which 
beginning at the vernal equinox, succeed each other 
eastward in the following order : 



NORTHERN 




SOUTHERN. 




1. Aries, . . . 


. . T 


7. Libra, . . . 


. *== 


2. Taurus, . . 


. . » 


8. Scorpio, . . . 


. *l 


3. Gemini, . . 


H 


9. Sagittarius, . , 


. t 


4. Cancer, . . 


. . 23 


10. Capricornus, . 


. V? 


5. Leo, . . . 


. . a 


11. Aquarius, . . 


. ~ 


6. Virgo, . . . 


. w 


12. Pisces, . . . 


. X 



The vernal equinox being at the first point of Aries, 
the summer solstice is at the first of Cancer, the 
autumnal equinox at the first of Libra, and the 
winter solstice at the first of Capricorn. 

13. Right Ascer&ion and Declination, — The right 
ascension of a heavenly body is the angular distance 
of its meridian from the vernal equinox, measured 
eastward on the equator. The declination of a body 
is its angular distance north or south from the equa- 
tor, measured on the meridian of the body. 

14L. Celestial Longitude and Latitude* — On the 

celestial sphere, longitude and latitude are referred to 
the ecliptic, not to the equator. Suppose a second- 
ary to the ecliptic to pass through a heavenly body ; 
the distance of the body from the ecliptic, measured 
on the secondary, is its latitude ; and the distance of 



12. What are signs of the ecliptic ? Name them in order. 

13. What is the right ascension of a body ? its declination ? 

14. Define celestial longitude and latitude. Which way is longi- 
tude reckoned ? right ascension ? 



BISING AND SETTING. 23 

this secondary, measured eastward on the ecliptic, is 
its longitude. 

Bight ascension and longitude are reckoned only 
eastward, from 0° to 360°, the first on the equator, 
the other on the ecliptic. 

15» Apparent Diurnal Motion of the Heavens. 

As the earth revolves from west to east on the axis ns, 
an observer, not being conscious of this motion, sees 
the heavenly bodies apparently revolving in the oppo- 
site direction ; that is, from east to west, about the axis 
NS. The sun, moon, and every planet, comet and 
star is observed to pass over from the eastern part of 
the sky toward the western, with a regular motion, 
reappearing again in the east, after the lapse of about 
one day, in the same, or nearly the same place. The 
fixed stars describe the circles, which are exactly 
parallel to the equator, and in precisely the same 
length of time. But the other bodies vary somewhat 
in their paths, and the periods of describing them, 
thus showing that they are affected by other motions 
besides the diurnal rotation. 

16* Kising, Setting, and Culmination* — In Fig. 4, 
AB, DO, FG, &c, drawn parallel to EQ, represent the 
diurnal circles of stars, viewed edgewise, and, there- 
fore, appearing as straight lines. Some of these 
circles intersect the horizon PIO. These intersections 
are the points of rising or setting. Thus, a star de- 



15. Explain the diurnal motion. 

16. What are the points of a body's rising and setting ? What 
are the points of its culmination ? Are both culminations ever in 
sight ? Are both ever out of sight ? 



24: THE EAETH. 

scribing the circle GF, rises in the northeast quarter, 
and sets in the northwest, at points which are both 
represented bj r. The star whose diurnal circle is 
IK, rises in the southeast, and sets in the southwest, 
at t. A star on the equator rises exactly in the east, 
and sets in the west, at the point 0. 

The points in which these circles cut the meridian 
are called the points of culmination. Thus, the star 
on FG makes its upper culmination at F, and its 
lower one at G. On AB, both the upper and lower 
culminations are above the horizon; on MP, they 
are both below. If both culminations of a star are 
above the horizon, it is always in view ; if both 
below, it never comes in sight. The number of stars 
which do not rise and set depends on the position of 
the celestial poles in relation to the horizon ; that is, 
on the latitude of the place. 

By the culmination of a body, in the ordinary use 
of the word, is meant its upper culmination. 

17 • Relations of the Horizon to the Diurnal Circles. 

Every change of position on the earth changes the 
horizon. If an observer moves eastward, all the 
heavenly bodies which rise and set rise earlier, and 
also culminate and set earlier. If he moves west- 
ward, they rise, culminate and set later. If he moves 
toward the nearer pole of the earth, the correspond- 
ing pole of the celestial sphere becomes more ele- 



17. Describe the effect of a person's moving east — west — toward 
the pole — toward the equator. Show what the elevation of one 
pole is equal to. Which pole is elevated ? How much is the other 

.? 



THE EIGHT SPHERE. 25 

vated, and the other more depressed ; and the con- 
trary, if he moves from the nearer pole ; that is, 
toward the equator. In all north latitudes, the north 
pole is elevated, and the south pole depressed ; and 
the reverse in south latitudes. And the elevation 
of one pole, and the depression of the other, equals 
the latitude. For (Fig. 4) NO, the elevation of one 
pole (= HS, the depression of the other), equals EZ, 
since each is the complement of ZN. But EZ == eo, 
the latitude, because they subtend the same angle 
atC. 

The elevation of the celestial equator equals the 
complement of latitude. For EH is the complement 
of EZ, which equals eo, the latitude. Hence, the 
angle by which all the circles of diurnal motion are 
inclined to the plane of the horizon, equals the com- 
plement of latitude, since they are parallel to the 
equator. 

On account of this change of inclination between 
the horizon and the diurnal circles, the aspect of the 
diurnal rotation is very different in different parts of 
the earth. 

18* The Might Sphere, — This name is given to 
those positions in which the diurnal circles cut the 
horizon at right angles. All points of the equator are 
so situated. As the latitude is zero, the poles, hav- 
ing no elevation or depression (Art. 17), are both in 
the horizon ; the celestial equator passes through the 
zenith, thus coinciding with the prime vertical ; and 
all the paths of daily motion, being parallel to the 



18/ Describe tlie right sphere. 



26 THE EAETH. 

equator, are perpendicular to the horizon. Every 
heavenly body, unless situated exactly at one of the 
poles, rises and sets during each revolution, and con- 
tinues above the horizon just as long as it remains 
below it, If a star rises in the east, it sets in the 
west, and culminates in the zenith and nadir. 

19. TJie Parallel Sphere, — This term expresses 
the appearance of the heavens at those points of the 
earth where the circles of daily rotation are par- 
allel to the horizon. This aspect can be presented 
only at the poles. For, at those points the latitude 
being 90°, one pole must be elevated 90°; that is, to 
the zenith, and the other depressed 90°, or to the 
nadir. Hence, the diurnal circles, being perpendicu- 
lar to the axis, must be horizontal, and the equator 
must coincide with the horizon. Every star in view 
passes around the sky, maintaining the same eleva- 
tion at every point of its path, and, therefore, never 
rises or sets. 

At the north pole, that half the year in which the 
sun is north of the equator, is uninterrupted day. 
During the other half, the sun being south of the 
equator, it is constant night. 

20. The Oblique Sphere. — At all latitudes, except 
0° and 90°, the circles of daily motion are oblique to 
the horizon, since they incline at an angle equal to 
the complement of the latitude. Thus, at 42° north 
latitude, the celestial equator is elevated 48° above 



19. Describe the parallel sphere. 

20. Describe the oblique sphere. What bodies are more than 
half the time above the horizon ? below ? 



ARTIFICIAL GLOBES. 27 

the southern horizon, as represented in Fig. 4 ; and 
all the diurnal circles, being parallel to the equator, 
make the same angle (48°) with the horizon. The 
circle OX), whose distance from the elevated pole 
equals its elevation, just touches the horizon at the 
lower culmination, and is the limit of that part of the 
sky which is always in view. This is called the circle 
of Perpetual Apparition. The circle HL, at the same 
distance from the depressed pole, also touches the 
horizon, and is called the circle of Perpetual Occulta- 
Hon, since it limits that part of the sky which is 
always concealed. 

The horizon HO bisects the equator EQ. Hence, 
a body on the equator is as long above the horizon as 
below it, in every part of the earth. But all bodies 
between the equator and the elevated pole are longer 
above the horizon than below, while on the opposite 
side they are longer below than above. 

21c Artificial Globes. — They are of two kinds, ter- 
restrial and celestial. The terrestial globe is a minia- 
ture representation of the earth, having, also, the 
equator and several meridians and parallels of lati- 
tude traced upon it. The celestial globe exhibits the 
principal fixed stars in their relations to each other, 
and to the equator and ecliptic. 

The artificial globe is suspended in a strong brass 
ring by an axis passing through the north and south 
poles, on which it is free to revolve. This ring repre- 
sents the meridian of any place, and is supported 



21. Describe the artificial globes. What is the quadrant of alti- 
tude? State the mode of adjusting the globe for the latitude. 



28 THE EAETH. 

vertically within a horizontal wooden ring which 
stands upon a tripod. The wooden ring represents 
the horizon. The brass ring may be slid around in 
its own plane, so as to elevate or depress either pole 
to any angle with the horizon. It is graduated from 
the equator each way to the poles, for measuring lati- 
tude and declination ; while the horizon ring has near 
its inner edge two graduated circles, one for azimuth, 
and the other for amplitude. On this ring, also, for 
convenient reference, are delineated the signs of the 
ecliptic, and the sun's place in it for every day of the 
year. 

Around the north pole is a small circle, marked 
with the hours of the day ; and at the same pole a 
brass index is attached to the meridian, which can be 
set at any hour of the circle. 

The Quadrant of Altitude is a flexible strip of brass, 
graduated into 90 parts, each equal to a degree of the 
globe. This can be used for measuring angular dis- 
tances in any direction on the sphere ; and when 
applied to a vertical circle of the celestial globe, it 
determines the altitude, or zenith distance of a heav- 
enly body. 

To adjust either globe for any place on the earth, 
elevate the corresponding pole to a height equal to 
the latitude. By moving the tripod, the axis can then 
be made parallel to that of the earth or the heavens. 
And if the globe is turned (the celestial westward, or 
the terrestrial eastward), the diurnal motion will be 
truly represented. 



22. Tell how to find the latitude and longitude of a place. The 
latitude and longitude of a place being given, how is it found? 



PROBLEMS. 29 

22* Problems on the Terrestrial Globe* 

1. To find tJie Latitude and Longitude of a Place. 

Turn the globe so as to bring the place to the brass 
meridian ; then the degree and minute on the merid- 
ian over the place shows its latitude, and the point of 
the equator, under the meridian, shows its longitude. 

Example. What are the latitude and longitude of 
New York ? 

2. To find a Place by its given Latitude and Longitude. 

Eind the given longitude on the equator, and bring 
it to the meridian ; then under the meridian, at the 
given latitude, will be found the required place. 

Ex. What place is in latitude 39° N., and longitude 
77° W. ? 

3. To find tlie Bearing and Distance of one Place from 
another 

Adjust the globe for one of the places, and bring 
it to the meridian ; screw the quadrant of altitude 
directly over the place, and bring its edge to the 
other place. Then the azimuth will be the bearing of 
the second place from the first, and the number of 
degrees beween them, multiplied by 69J, will give 
their distance apart in miles. 

Ex. Find the bearing of New Orleans from New 
York, and the distance between them. 



How is the bearing of one place from another found? Find the 
difference of time at different places. When it is 2 P. M. in Paris, 
what time is it in Boston ? 



30 THE EAETH. 

4. To find the Difference of Time at Different Places. 

Bring to the meridian the place which lies west of 
the other, and set the hour-index at XII. Turn the 
globe westward, until the other place comes to the 
meridian, and the index will show the hour at the 
second place when it is noon at the first. The hour 
thus found is the difference required. 

Ex. "When it is noon at New York, what time is it 
at London ? 

5. The Hour being given at any Place, to find ivhat Hour 
it is at any other Place. 

Find the difference of time between the two places, 
as in (4) ; then, if the place whose time is required is 
east of the other, add this difference to the given 
time ; but if west, subtract it. 

Ex. What time is it in Boston, when it is 2 P. M. in 
Paris ? 

23, Problems on the Celestial Globe. 

1. To find the Right Ascension and Declination of a 
Heavenly Body. 

Bring the place of the body to the meridian ; then 
the point directly over it shows its declination, and 
the point of the equator under the meridian, its right 
ascension. 

Ex. Find the right ascension and declination of 
Alpha Lyrse. Also, of the sun on the 3d of May. 



23. How are the riglit ascension and declination of a star found ? 
Describe the manner of adjusting tho globe to represent the heav- 



PROBLEMS. 31 

2. To Represent the Appearance of the Heavens at any 

Time. 

Adjust the globe for the place (Art. 21). On the 
wooden horizon find the day of the month, and 
against it is given the sun's place in the ecliptic. On 
the ecliptic find the same sign and degree, and bring 
the point to the meridian. The globe then presents 
the positions of the stars at noon. Set the hour- 
index at XII, and turn the globe till the index points 
to the required hour. The aspect of the heavens at 
that hour is then represented. 

Ex. Kequired the aspect of the stars at Lat. 51°, 
December 5th, at 10 P. M. 

3. To find the Time of the Rising and Setting of any 

Heavenly Body at a given Blace. 

Having adjusted for the latitude, bring the sun's 
place in the ecliptic to the meridian, and set the 
index at XII. Turn the globe eastward, and then 
westward, till the given body meets the horizon, and 
the index will show the times of rising and setting. 

The times of the sun's rising and setting may be 
found in the same manner on the terrestrial globe, 
since the ecliptic is usually represented on it. 

Ex. At what time does the sun rise and set on the 
4th of July? 

Eind the time of the rising and setting of Arcturus 
on the 10th of November. 



ens at a given time. How are the times of rising and setting of a 
body found ? How are the altitude and azimuth of a body found ? 
The distance between two stars ? Find the height of the sun at 
noon, August 1st, Lat. 28° 30' N. 



32 THE EARTH. 

4. To find the Altitude and Azimuth of a Star for a given 
Latitude and Time. 

Adjust the globe for the aspect of the heavens (2) ; 
screw the quadrant of altitude to the zenith, and 
direct it through the place of the star ; then, the arc 
between the star and the horizon is the altitude, and 
the arc of the horizon between the quadrant of alti- 
tude and the meridian is the azimuth. 

Ex. Find the altitude and azimuth of Sirius, De- 
cember 25th, at 9 p. m. Lat. 43°. 

5. To find the Angular Distance between two Stars. 

Lay the quadrant of altitude across the two stars, 
so that the zero shall fall on one of them ; then, the 
degree at the other will show their distance from each 
other. 

Ex. Find the distance between Arcturus and Alpha 
Lyrae. 

6. To find the Suns Meridian Altitude for a given Lati- 
tude and Day. 

Find the sun's place, and bring it to the meridian. 
The degree over it will show its declination. If the 
declination and latitude are both north or south, add 
the declination to the co-latitude ; if not, subtract it. 

Ex. Find the sun's meridian altitude at noon, Aug. 
1st, Lat. 38° 30' K 



CHAPTEE II. 

PARALLAX — ATMOSPHERIC REFRACTION — TWILIGHT. 

24. Parallax Defined. — When a person changes 
his place, objects about him in general appear in dif- 
ferent directions from him. This change of direction 
is called Parallax. If, for example, he moves north, 
an object which was directly ivest of him is moved by 
parallax towards the soidhivest ; and an object which 
was east now appears in the southeast quarter. The 
direction of every thing is more or less altered, 
except those objects which are directly before, or 
directly behind him. 

It is easily perceived, also, that objects which are 
near change their direction very rapidly ; while distant 
things change slowly, or even appear to remain at 
rest, unless the person moves a great way. The par- 
allax of a body may, therefore, be used to enable us 
to find out how far off it is. 

25. Diurnal Parallax. — While a person travels 
over the earth, or is carried about it by the diurnal 
rotation, the heavenly bodies must in the same way 
suffer some change of direction. 



24. Define parallax. Illustrate it. Compare near and distant 
objects. 



34 



THE EARTH. 



By the true place of a heavenly body is meant that 
which it would seem to occupy if viewed from the 
center of the earth. At the surface, therefore, it ap- 
pears generally displaced from its true position ; and 
this displacement is called the Diurnal Parallax, 




Thus, the true place of the "body M (Fig. 5) is in the 
direction CK ; but at A it appears in the line AH ; 
and the parallax is the angle AMO. So, the true 
place of M is Q, its apparent place is P, and the par- 
allax is AM'C. But the body M"' appears at Z, 
whether viewed from A or C, and the parallax in 
this case is zero. Since the earth's radius, in each 
instance, subtends the angle of parallax, we have the 
following definition : 

The diurnal parallax of a body is the angle at that 
body subtended by the semi-diameter of the earth. 



25. What is diurnal parallax ? What is the true place of a body ? 
Show the effect of parallax by the figure. 



ATMOSPHEEIC EEFKACTION. 35 

2G* On what Diurnal Parallax Depends. — At the 

horizon, the angle M, being subtended perpendicu- 
larly by the earth's radius AC, is larger than M', or 
M", which are subtended obliquely. And it is plain, 
that the higher the body in the sky, the less is its 
parallax, till at M m , when seen in the zenith, it has 
no parallax at all. 

Again, if the body were further removed from the 
earth, it is obvious that the angle M, subtended by 
the same line AC, would be smaller. Hence, the par- 
allax of a body is greatest at the horizon, and varies in- 
versely as the distance of the body from the earth's center. 

The parallax of a body at the horizon is called its 
Horizontal Parallax. 

7. TJie Parallax of the 3Ioon. — There is no one 
of the heavenly bodies which has so great a parallax 
as the moon. It is, therefore, the nearest of them all. 
But even the moon's parallax is less than one degree; 
that is, if a person were to travel over the line AC, 
which is about 4,000 miles long, the direction of the 
moon would not be changed so much as one degree. 
This shows that the moon, though nearer than any 
other body, is yet at a very great distance from us. 

28* Atmospheric Hefraction. — The atmosphere of 
the earth refracts or bends the rays of light as they 
come through it from the heavenly bodies. Let DD 
(Fig. 6) be a part of the surface of the earth, and AA 



20. On what does parallax depend? Where is it nothing? 
Where is it greatest ? What i3 it called ? 

£7. What heavenly body has the greatest parallax ? How much ? 



36 



THE EAKTH 



the top of the atmosphere. If a person is at O, the 
light of the star S does not come to hLn in a straight 
line, but first strikes at a, and is bent downward to b, 
then to c, and finally to O. Therefore it does not 
seem to come from S, but from S', in the line Oc pro- 
duced. Thus, the star appears elevated above its 




ABCD DOBA 

true place. In this figure, the effect of refraction is 
very much exaggerated. The greatest refraction 
takes place at the horizon ; but even there it elevates 
an object only about 34', or a little more than the 
breadth of the sun. As the height above the horizon 
increases, the refraction becomes less, and is nothing 
at the zenith. 



29* Time of Rising and Setting Affected by Re- 
fraction. — Since a body at the horizon appears raised 



28. Show by the figure how light from a star comes to a person. 
What effect is produced? Where is refraction greatest? How 
much is it ? 



ILLUMINATION OF THE SKY. 37 

above its true place about the breadth of the sun or 
moon, it must appear to rise earlier and to set later 
than it really does. This circumstance causes the 
sun and all the bodies which rise and set to be seen 
above the horizon at least four minutes longer than 
they would do if there were no atmosphere. 

30, Distortion of the Sun's and Bloon's Disk by 
Refraction. — The change in the amount of refraction 
is so rapid near the horizon, that when the sun has 
just risen, or is just about to set, the lower limb is 
elevated more than the upper by a very perceptible 
quantity. Its form, therefore, does not appear circu- 
lar, but nearly elliptical, the vertical diameter being 
shortened about 5' or 6'. The lower half, however, 
appears more flattened than the upper half, because 
the difference of refraction between the lower limb 
and the center is greater than that between the center 
and the upper limb. 

SI, Illumination of the Sky. — During the day the 
atmosphere is illuminated by the light of the sun, 
which penetrates every part of it, and is reflected in 
all directions. If there were no air, the sky, instead 
of appearing luminous by day, would exhibit the 
same blackness as by night, and the stars would be 
visible alike at all times. "We should, in that case, 
lose a great part of that generally diffused light 
which illuminates the interior of buildings and other 



29. Its effect on the time of rising and setting ? 

30. Describe and explain the effect on the disk of the sun. 

31. How would the sky appear if there were no air ? Why ? 



38 THE EAETH. 

places screened from the direct rays of the sun. The 
earth's surface, and all terrestrial objects on which 
the sunlight falls directly, would indeed, by radiant 
reflection, cause a degree of illumination, but it would 
be far less than we now enjoy. It has been observed, 
in ascending to great heights, either on mountains or 
in balloons, where, of course, the air which is most 
dense and reflects most abundantly is left below, that 
the sky assumes a very dark hue, and the general 
illumination is greatly diminished. 

32, Twilight. — The illumination of the sky begins 
before the sun rises, and continues after it sets. It is 
then called twilight. More or less of it is visible as 
long as the sun is not more than 18° vertically below 
the horizon. Those parts of the atmosphere are 
most luminous which lie nearest to the direction of 




the sun. Thus, in Fig. 7, let A be a place on the earth 
where the sun is just setting. The whole sky, IEFH, 
is illuminated. But, to a place further east, as B, the 
twilight extends from E to H, the part of the sky 
HK, remote from the sun being in the* shadow of the 



32. Explain twilight by Fig. 7. 



DUBATION OF TWILIGHT. 39 

earth. At C, only FH is illuminated, and HL is 
dark. At D, the twilight is entirely gone. 

Though the twilight terminates at H, there is no 
abrupt transition from light to shade at that point, 
since the reflection from those high and rare parts of 
the air is exceedingly feeble ; and, also, because the 
thickness of the illuminated segment, through which 
we look, diminishes gradually to that limit, as is obvi- 
ous from an inspection of the figure. 

S3. Duration of Twilight. — To an observer at the 
equator, at those times of the year when the sun is 
on the celestial equator, the twilight continues Ih. 
12m. For, in the diurnal motion, 15° are described 
in an hour, and, therefore, 18° in l^h. = lh. 12m. 
This is the shortest duration possible. For, if the 
sun were north or south of the equator, the degrees 
of diurnal motion would be shorter than those on a 
great circle. And, if the observer were on some par- 
allel of latitude, the circles of daily motion would be 
oblique to his horizon, and the sun must, therefore, 
pass over more than 18° in order to move 18° verti- 
cally. An extreme case occurs at the poles, where 
twilight lasts several months. 



33. How long does it last in different cases. 



CHAPTEE III. 

ASTRONOMICAL INSTRUMENTS- 

THE SUN — THE SEASONS — FOKM OF THE EARTH'S ORBIT. 

34, The Equatorial Telescope. — In order that the 
telescope may be used to the best advantage for 
astronomical purposes, it is often mounted equator- 
idtty ; that is, it can be turned on tivo axes, one par- 
allel to the earth's axis, and the other perpendicular 
to it. And, besides this, a clock is connected with 
the first axis in such a way as to revolve the telescope 
just as fast as the earth revolves, and in the opposite 
direction. Thus, any heavenly body to which the 
telescope is directed remains steadily in the field of 
view, and can be examined leisurely and with care. 

35. The Transit Instrument. — This is a telescope 
so mounted as to observe a heavenly body at the 
instant when it crosses the meridian. AD (Fig. 8) 
represents the telescope supported by a horizontal 
axis, which consists of two hollow cones placed base 
to base, so as to combine lightness and strength. 
The ends of the axis rest in sockets, attached to two 
stone piers, E and W. That the instrument may re- 
ceive no tremors from the building, the piers stand 



34. Describe the equatorial telescope. Why so mounted ? 



ASTEONOMICAL INSTKUMENTS 



41 



on a firm foundation in the ground, passing through 
the floor without contact. The axis being placed east 
and west horizontally, the telescope, which is perpen- 
dicular to it, will, when turned, revolve in the plane of 



Fig. 8. 




the meridian. A graduated circle, N, is attached to 
one end of the axis, for marking altitudes or zenith 
distances. The whole instrument can be raised from 
the sockets, and the axis inverted, so that the east 
end shall rest on the pier "W, and the west end on the 



35. Describe the transit instrument.. Why so called ? 



42 THE SAETH. 

pier E. In the focus of the eye-glass there is a fine 
horizontal wire, and several vertical wires, of which 
the middle one is on the meridian. "When a star 
which is crossing the field of view is seen on the 
middle wire, it is at that moment making a transit of 
the meridian. 

SO. TJie Astronomical Clock. — A clock must be 
near the transit instrument, to show the exact time of 
the transit. The clock of the observatory is made to 
keep sidereal time ; that is, star time instead of sun 
time. One sidereal day is the length of time from 
the moment a star passes the meridian till it passes 
it again ; and it is about four minutes shorter than a 
day as measured by the sun. The sidereal day be- 
gins and ends at the moment when the vernal equinox 
is on the meridian. 

37* To find the Might Ascension and Declination 
of a Heavenly Body. — Observe the exact sidereal 
time when the body makes its transit. That time ex- 
presses its right ascension, or its distance east of the 
vernal equinox, in hours, minutes, and seconds. This 
may be changed into degrees, minutes, and seconds. 
For, since a star makes an apparent revolution of 
360° in 24 sidereal hours, it describes 15° in one hour, 
15' in one minute, and 15" in one second. Bight 
ascension is measured either in time or in arc. 

The declination of the body is found by observing 



36. What accompanies it ? Wliat kind of time is kept ? 

37. State "how to find the right ascension of a body. In what 
denominations is it measured? How is its declination found? 
What other instrument is sometimes used for this? 



ASTRONOMICAL INSTRUMENTS 



43 



its height above the horizon, as indicated on the 
circle N, and then finding the difference between this 
height and the height of the equator, which is known 
by the latitude of the place. A separate instrument, 
called the Mural Circle, is sometimes employed in the 
observatory for finding the declination. 

38* The Altitude and Azimuth Instrument. — The 

essential parts of this instrument are a telescope and 
two graduated circles, one vertical, the other horizon- 

Fra. 9. 




tal. Fig. 9 presents one of its more simple forms. 
The telescope AB is movable on a horizontal axis, 



88. Describe the altitude and azimuth instrument, and its use. 



44 THE EARTH. 

at the center of the vertical circle abc, and also on a 
vertical axis, passing through the center of the hori- 
zontal circle EFG. The levels g and h, placed at 
right angles to each other, show when the circle EFG 
is brought to a horizontal position by the tripod 
screws. The tangent screws, d and e, give slow mo- 
tions, one in a vertical, the other in a horizontal plane. 
If the reading of the vertical circle is taken when the 
telescope is horizontal, and again when it is directed 
to a star, the difference of the readings is equal to the 
altitude of the star. In a similar manner, if the hori- 
zontal circle is read when the telescope is directed to 
the north, and read again when it is directed to a 
star, the difference is its azimuth. 

39o The Sextant. — This is an instrument for meas- 
uring the angular distance between two points situ- 
ated in any plane whatever. It is represented in Fig. 
10. I and H are two small mirrors, and T a small 
telescope. ID is a movable radius or index, carrying 
the index mirror at the center of motion, I, and a 
vernier at the extremity, D. The horizon glass, H, is 
silvered only on one-half of its surface. When the 
zero of the vernier coincides with that of the arc at 
F, the mirrors are precisely parallel. If now we 
direct the telescope to a star, it may be seen in the 
transparent part of the horizon glass, and its image 
in close contact with it, in the silvered part. 

In order to measure an angle, as, for example, that 
between the moon M and the star S, direct the tele- 



39. Describe the sextant, and how to measure the distance be- 
tween the mocn and a star. 



THE SUN'S PLAGE, 
Fig. 10. 



45 




scope to S, and turn the index from F toward E, till 
the moon is seen to touch the star. The vernier will 
then show on the graduated arc the size of the angle 
between the star and the moon's limb. 

40, Observations of the Sun's Place. — If we em- 
ploy the instruments of the observatory in measuring 
from day to day the right ascension and declination 
of the sun, at the moment of its crossing the merid- 
ian, it will be discovered that these quantities are 
constantly changing ; or, in other words, that the sun 
is constantly shifting its place in relation to the stars. 



40. What motion has the sun in right ascension ? What in de- 
clination? When is It furthest north? When furthest south? 



46 THE EAETH. 

In right ascension, the sun gains nearly a degree 
every day ; that is, it moves eastivard nearly a degree 
each day ; so that, in 365 or 366 days, it comes round 
again to the same place among the stars. 

But in declination, it moves alternately north and 
south, crossing the equator on the 21st of March, as 
it moves northward, and again on the 22d of Septem- 
ber, as it returns southward. On the 22d of June it 
is furthest north, and on the 22d of December it is 
furthest south. Its greatest distance north and south 
of the equator is about 23 J°. 

41. The Ecliptic and Zodiac* — The apparent an- 
nual path of the sun is found, by the foregoing ob- 
servations, to lie in a ptarw, cutting the celestial sphere" 
in a circle called the Ecliptic (Art. 11), and inclined to 
the plane of the equator at an angle of about 23° 27'. 

The Zjdiac is the name given to a zone of the 
heavens, 16° wide, extending along the circle of the 
ecliptic, 8° on each side of it. The paths of the prin- 
cipal planets lie within this zone. Its length is 
divided into 12 signs of 30° each, having the same 
names and arranged in the same order as those of 
the ecliptic (Art. 12), though not coincident with 
them. The signs of the zodiac are distinguished 
from each other by the stars which occupy them. 

42. The Tropics and Polar Circles. — Through the 
two points of the ecliptic most distant from the equa- 



Wlien does it cross the equator ? How far north, and how far south 
does it go ? 

41. How does the sun's path lie? What is the zodiac? How 
divided ? 



THE ANNUAL MOTION. 47 

tor, called the solstices, (Art. 11), we imagine circles 
to be drawn parallel to the equator, called the Tropics. 
The northern circle, passing through the first of Can- 
cer on the ecliptic, is called the tropic of Cancer ; the 
southern one, for a like reason, is called the tropic of 
Capricorn. Two other parallels to the equator, pass- 
ing through the poles of the ecliptic, and therefore 
23° 27' from the poles of the equator, are called the 
Polar Circles. 

43. Terrestrial Zones. — On the terrestrial sphere, 
a similar system of circles divides the earth's surface 
into the well-known zones of geography, called the 
torrid, temperate, and frigid zones. The tropics are 
the limits of vertical sunshine in mid-summer. The 
polar circles are the limits within which the sun 
makes a diurnal revolution in mid-summer and mid- 
winter without rising or setting. 

44:, The Annual Motion Observed without Instru- 
mentsm — If the stars were visible in the daytime, we 
should perceive the sun making progress among them 
toward the east, by a distance equal to nearly twice 
its own breadth every day, since the apparent diame- 
ter of the sun is a little more than half a degree. 
But, as they are invisible by day, we detect the same 
fact, when we notice that at a given hour of the night 
all the stars are further west than on a previous night. 
For example, at 9 o'clock p. m. — that is, 9 hours after 



42. Define the tropics — the polar circles. 

43. The zones of the earth. 

44. How is the annual motion of the sun perceived without in- 
struments? How far each day does it move ? 



48 



THE EAETH. 



noon — it is easily observed that there is, from one 
evening to another, a regular progress of all the stars 
westward, as long as we choose to watch them. In 
other words, the sun is at the same rate advancing 
eastward relatively to the stars. 

43. The Annual 3Iotion is a Motion of the Earth, 
not of the Sun. — There is abundant evidence that the 
motion of the sun around the earth, above described, 
is only apparent, and results from a real motion of the 
earth about the sun. Thus, suppose the earth to pass 

Fig. 11. 




around the sun S (Fig. 11) in the orbit ABPC, in the 
order of the signs. If we were unconscious of this 
motion, the sun would appear to us to move about 



45. Is this really the sun's motion ? Use Fig. 11. 



CHANGE OF SEASONS. 49 

the earth in the same order of the signs, though, 
at any given moment, in a contrary direction. When 
the earth is at B (in the sign T, as seen from the 
sun), we could see the sun in the sign ^= ; when we 
reach b , the sun is seen in fit ; and so on. 

46. Catise of the Change of Seasons. — The phe- 
nomena of the seasons are due to the fact that the 
two revolutions of the earth, one on its axis, and the 
other around the sun, are in different planes ; in other 
words, that the equator and the ecliptic make an 
angle with each other. In Fig. 12, let the ecliptic be 
represented by the large circle in the plane of the 
paper. And suppose the earth to pass round the sun 
in the order of the signs, °P, s , n, etc., occupying the 
position A on the 21st of March, B on June 22d, C on 
September 22d, and D on December 22d. 

Next, suppose the plane of the equator (represented 
by the straight line eq) to be inclined to the plane of 
the paper by an angle of 23J°, and always in the 
same direction. The axis ns, which is perpendicular 
to eq, will, therefore, be parallel to itself in all posi- 
tions of the earth. In the figure, it is represented as 
everywhere leaning to the right. At A, the earth's 
position, March 21st, the rays of the sun just reach to 
n and s ; so that, if the earth revolves on ns at that 
place, every spot on its surface will be one-half the 
time in the light, and the other half in darkness. 
The days and nights are, therefore, equal. In this 
position, the plane eq, if extended, passes through 



46. By Fig. 12, show how the seasons are caused. Position A ; 
position B, C, D. 

3 * 



50 



THE BAETH. 



the sun; that is, the sun is in the equator of the 
heavens, and it is the time of the vernal equinox. 



Fig. 12. 




In the position B, the circle of illumination, as 
represented, reaches beyond n to the polar circle, and 
falls short of s by the same distance, the sun being 
seen north of the equator eq. As the earth revolves 
on ns, it is evident that all places north of eq are 
longer in light than in darkness ; and the reverse is 
true of all places south of eq. It is now summer in 
the northern hemisphere, and winter in the southern. 



HEATANDCOLD. 51 

At C, the earth has reached the autumnal equinox ; 
the circle of illumination passes through n and s, and 
the phenomena are the same as at A. 

At D, the north pole is turned as far as possible 
into the shade, and the south pole into the sunlight. 
The sun is at the tropic of Capricorn ; and as the 
earth rotates on ns 9 all places north of the equator 
experience the short days and the long nights of 
winter, and the reverse at all places south of the 
equator. 

47 • Causes of Seat in Summer and Cold in Win- 
ter. — These are two. 

1st. The length of the day compared with the 
night. The heat of the earth is passing off by radi- 
ation during the whole time, whether the sun shines 
or not. But the earth receives heat from the sun 
only while the sun is above the horizon. Hence, the 
longer the period of sunshine, compared with the 
time of a diurnal revolution, the greater the heat. 
For this reason, therefore, the summer is warmer 
than the winter. 

2d. The greater altitude of the sun in summer than 
in winter. The greater the sun's height is, the more 
numerous are the rays which fall on a given area. 
Between March and September the northern hemi- 
sphere has its summer, both because the days are 
longest and the sun is highest. And for a similar 
reason the southern hemisphere has its summer be- 
tween September and March. Of course the winter 



47. Give the first reason for heat in summer, and cold in winter, 
the second. 



52 THEEAETH. 

of each hemisphere occurs at the same time as the 
summer of the other. 

48. Wliy the Greatest Heat is Later than the Sum- 
mer Solstice, and the Greatest Cold Later than the 
Whiter Solstice. — If the sun sheds on a given surface 
more heat each day than the surface loses by radi- 
ation, then the heat accumulates from day to day. 
This is the case during the long days of summer; and 
more heat is gained than lost till a month or more 
after the summer solstice. For a like reason, during 
the middle hours of the day, heat is received from 
the sun more rapidly than it is lost by radiation, so 
that the hottest hour is 2 or 3 o'clock p. M. 

In the winter, on the contrary, the loss by radiation 
exceeds the quantity received from the sun during all 
the shortest days, so that the temperature descends 
till many weeks after the winter solstice. 

49» iVo Change of Seasons if there were no Obli- 
quity. — The angle between the planes of the two mo- 
tions of the earth being the cause of the change of 
seasons, it follows that there would be no such change 
if those motions were in the same plane. If, while 
the earth advances in its orbit about the sun, it should 
rotate in the same direction on its axis, then the sun 
would always be in the plane of the equator, and 
would, every day of the year, describe the equator as 
its diurnal circle, rising exactly in the east, culmi- 



48. Why is it hottest after the longest days ? Why coldest after 
the shortest days ? 

49. If the ecliptic coincided with the equator, what would be the 
seasons ? 



FORM OF THE EARTH'S ORBIT. 53 

nating at a zenith distance equal to the latitude of 
the place, and setting exactly in the west. At the 
equator, the sun would always follow the prime verti- 
cal, and at either pole it would always be passing 
round in the horizon. 

oO» The Greatest Changes of Season if the Obli- 
quity were 90\ — If, while the earth revolves on its 
axis from west to east, it should pass around the sun 
in a plane lying north and south, then the ecliptic 
would pas§ through the north and south poles, and 
the solstices would be at the poles. Hence, at a 
station on the equator, the sun would, during the 
year, describe the prime vertical and various small 
circles parallel to it, down to the north and south 
points of the horizon, where it would be stationary 
alternately at the times of the solstices. At the 
equator, therefore, there would be an alternation from 
summer to winter, or the reverse, every three months. 

SI • Mode of Determining the Form of the JEqrth's 

Orbit. — The earth's orbit is an ellipse described 
about the sun, which is situated in one of its foci. 
This is ascertained by observing the changes in the 
sun's apparent diameter throughout the year. "When 
the sun appears smallest, it is most distant; and 
when largest, it is nearest. And its distance, in all 
cases, varies inversely as its apparent diameter. 
Therefore, if the sun's apparent diameter be accu- 
rately measured as frequently as possible, we can 
from these measurements find the relative distances ; 
and these distances determine the form of the orbit. 



50. What if the obliquity were 90°? 



54 



THE EAETH. 



Thus, suppose the earth to be at E (Fig. 13), and 
that the sun's apparent diameter is measured when in 
the direction Ea. After it has advanced eastward 
some days, so as to be seen in the direction E6, let it 
be measured again : and so on, at every opportunity 
through the year. Then the proportion of the lines 

Fig. 13. 




Ea, W), Ec, etc., will be known ; and if they are laid 
down of the proper length, and in the proper direc- 
tions, the dotted line abmv, passing through their 
extremities, will be the true form of the sun's ap- 
parent orbit about the earth, and, therefore, of the 
earth's orbit about the sun. This form is found to 
be an ellipse, having the sun in one of its foci. 

52. Definitions Relating to a Planetary Orbit, 

Let E be the focus occupied by the sun, and am the 



51. What observations are made to find the form of the earth's 
orbit ? Describe by the figure. What is the form ? 



LINE OE APSIDES. 55 

the major axis of an elliptical orbit described about 
it ; the nearest point, a, is called the 'perihelion, and the 
most distant point, m, the aphelion. The two points 
a and m are also called the apsides. The varying dis- 
tance, Ea, E&, Wi, etc., is called the radius vector. If 
the major axis, am,, is bisected in C, the ratio of EG 
to the semi-major axis, aC, is called the eccentricity of 
the orbit. The less EC is, compared with aC, the 
less is the eccentricity, and the nearer does the ellipse 
approach to a circle. If E coincides with C, the 
eccentricity is nothing, and the orbit is a circle. 

The eccentricity of the earth's orbit is only g 1 ^ ; 
that is, EC is ^ of aC. If the figure were drawn in 
that proportion, it could not be distinguished from a 
circle. 

53, Position of the Line of Apsides. — The direc- 
tion of the major axis of the earth's orbit, or the line 
of apsides, is slowly changing ; but at present it 
passes through the 10th degree of Cancer and Capri- 
corn, as represented in Eig. 11. The earth is at peri- 
helion on the 1st of January, and at aphelion on the 
1st of July. We are, therefore, nearest to the sun in 
the winter of the northern hemisphere, and furthest 
from it in the summer. 

54. Distance from the Sun, as Affecting the Sea- 
sons. — The intensity of the sun's heat at the earth, as 
well as that of its light, varies inversely as the square 



52. Define the several parts of an orbit. How much is the eccen- 
tricity of the earth's orbit ? It is nearly of what shape ? 

53. When does the earth pass the perihelion and the aphelion ? 



56 THE EAETH. 

of our distance from it. On this account, the inten- 
sity of heat at perihelion is to that at aphelion as 
6V : 59 3 , which is nearly as 31 : 29. Therefore, so 
far as distance is concerned, the earth receives -^- s 
more heat on the 1st of January than on the 1st of 
July. This produces a slight effect to mitigate the 
severity of cold in winter and of heat in summer, 
in the northern hemisphere, and to aggravate the 
same in the southern hemisphere. 



54. Why is it not colder when we are furthest from the sun ? 



CHAPTEE IY. 

SIDEEEAL TIME — MEAN AND APPAEENT SOLAE TIME — 
THE CALENDAE. 

££• Hie Sidereal Day. — This is the interval of 
time which elapses between two successive culmina- 
tions of a star (Art. 36). The length of this interval 
appears to be invariable, whatever star is observed, 
or in whatever season or year the observation is 
made. On this account, the sidereal day is regarded 
as the true period of the earth's rotation on its axis. 
In order to reckon by sidereal time, the moment 
chosen for the beginning of each sidereal day is the 
moment when the vernal equinox culminates. The 
sidereal clock, if correct, then points to 0/?. 0m. 0s. 
Each sidereal day is divided into 24 sidereal hours, 
each hour into 60 sidereal minutes, and each minute 
into 60 sidereal seconds. 

£8. Hie Mean Solar Bay. — This is the mean in- 
terval between two successive culminations of the 
Sun. It will be shown, presently, that these inter- 
vals vary throughout the year. As the sun, by the 
annual motion, is advancing eastward continually 



55. What is a sidereal day ? When does it begin ? 

56. What is the mean solar day ? How does it differ from the 
sidereal day? 



58 THE EAETH. 

among the stars, the solar day must always be longer 
than the sidereal day. For, if the sun and a star 
were on the meridian of a place together, then, while 
that place passes around eastward till its meridian 
meets the star again, the sun has advanced eastward 
nearly a degree, and the place must revolve nearly a 
degree more than one revolution before its meridian 
will reach the sun. This will require nearly 4 minutes 
of time ; for, in the diurnal motion, 15° correspond 
to one hour, and, therefore, 1° to -^ of an hour ; that 
is, 4 minutes. 

«57. The Apparent Solar Day. — This is the actual 
interval between two successive culminations of the 
sun. And this interval changes its length from day 
to day through the entire year, being sometimes 
greater and sometimes less than the mean solar day. 

In keeping solar time by clocks and watches, it is 
customary, for convenience, to aim to keep the mean 
rather than the apparent time, and to regard the sun 
as going alternately too fast and too slow. 

$8, Causes of Unequal Solar Daus. — After the 
earth has completed a sidereal day, it must always 
revolve a little further to bring the meridian of a 
place to the sun, which has advanced nearly one 
degree eastward. Now, if the sun advanced east- 
ward exactly the same distance every day, then the 
solar days, as well as the sidereal days, would all 



57. What is the apparent solar day ? Which is used in keeping 
time? 

58. What makes the solar days unequal ? 



CIVIL AND ASTRONOMICAL TIME. 59 

be equal. But it does not ; for sometimes the annual 
motion is faster, and sometimes slower; and some- 
times it is parallel to the daily motion, and again it is 
oblique. Hence, the arc of right ascension, to be 
added to the sidereal day in order to complete the 
solar day, varies in its length ; and, therefore, the 
solar days themselves must be of different lengths. 

S9. The Equation of Time. — The difference be- 
tween mean time and apparent time, on any given 
day, is the equation of time for that day. If the sun 
is slow, the equation must be added to the apparerst 
time ; if fast, it must be subtracted, in order to give 
mean time. The mean and apparent time agree four 
times in a year — April 15th, June 15th, September 
1st, and December 24th. The two largest equations 
are, +14 minutes, February 11th, and —16 minutes, 
November 2d. 

S0» Civil and Astronomical Time* — -The mean 
solar day, when employed for civil purposes, is sup- 
posed to begin and end at midnight, and is divided 
into hours, numbering from 1 to 12 A. M., and then 
from 1 to 12 P. M. But the astronomical day (which is 
also the mean solar day) begins and ends at noon, 12 
hours later than the corresponding civil day, and its 
hours are counted from 1 to 24. Thus, the astronom- 
ical date, April 12c/, 207*., is the same as the civil date, 
April 13th, 8 o'clock A. m. 



59. What is tlie equation of time ? How large does it ever be- 
come ? 

60. State the diffsrencs between civil and astronomical time. 



60 THE EARTH. 

Gl, Tlie Julian Calendar. — The period in which 
the sun passes from the vernal equinox to the same 
point again, is called the Tropical Year. In that 
period the round of the seasons is exactly completed. 
The length of the tropical year is 365c?. 5h. 4.8m. 
46.155. This is so near 3 65 J days, that in the adjust- 
ment of the calendar made by Julius Caesar (hence 
called the Julian calendar), three successive years 
were made to contain 365 days each, and the fourth 
366 days. The additional day is called the intercalary 
day. In this calendar it was introduced by reckoning 
twice the 6th day before the Kalends of March ; and 
hence the year containing this additional day was 
called the Bissextile. The intercalary day is now the 
29fch of February, and the year containing such a day 
is called Leap Year. 

62. The Gregorian Calendar. — By calling the 
tropical year 365 \ days, the Julian calendar makes it 
more than 11 minutes too long, and the intercalation 
of one day in four years is, therefore, too great. 
This excess amounts to more than 18 hours in a cen- 
tury. Hence, by dropping the intercalary day three 
times in four centuries, the adjustment is nearly com- 
plete. The Julian calendar, thus amended, is called 
the Gregorian calendar, because adopted under Pope 
Gregory XIII. At that time, 1582, the vernal equi- 
nox, by the error of the Julian calendar, had fallen 



61. What is the tropical year? Describe the Julian calendar. 
What is meant by leap year ? 

62. What was the defect in the Julian calendar ? Describe the 
Gregorian calendar. Will it always be correct? What is old 
style? 



HOW TO COMPAEE DAYS. 61 

back to March, 11th. To bring the equinox to its 
proper date, 10 days were first dropped (the 5th being 
called the 15th), and then the following system was 
adopted : 

Every year not exactly divisible by 4, has 365 
days. 

Every year divisible by 4, and not by 100, has 366 
days. 

Every year divisible by 100, and not by 400, has 
365 days. 

Every year divisible by 400, has 366 days. 

The Gregorian calendar will not be correct perpet- 
ually, but the error will not amount to a day in 4,000 
years. 

The nation of Russia has not yet adopted the Gre- 
gorian calendar, so that there is now a discrepancy of 
12 days between their dates and those of other na- 
tions. The reckoning still used by them is known as 
Old Style, and is distinguished by appending the let- 
ters O. S. to every date. 

OS. JEEoiv to Compare Days of the Month and of 
the Week in Passing from one Year to Another, — A 

common year of 365 days contains 52 weeks and one 
day ; a leap-year contains 52 weeks and two days. 
Hence, a year usually begins a day later in the week 
than the year previous. And, generally, any day of 
any month is one day later in the week than the same 
day of the preceding year. Thus, July 4th, 1365, 



63. What is tlie change in a given day of the month, in passing 
from one year to another? Why does it fall a day later in the 
week ? When does it fall two days later, and why ? 



62 THE EAETH. 

falls on Tuesday; 1866, on "Wednesday; 1867, on 
Thursday. But, in leap-year, this rule applies only 
till the end of February. From that time to the 
same date in the year following, every day of a 
month falls two days later in the week than in the 
previous year. Thus, July 14th, 1871, is Tuesday ; 
1872, Thursday ; and February 22d, 1872, is Thurs- 
day ; 1873, it is Saturday. 



CHAPTEE V. 

OBLATE FORM OF THE EAETH — ITS MASS AND DENSITY — 
PKOOFS OF ITS ROTATION ON AN AXIS. 

64. Central Forces. — When a body is revolving on 
an axis, the parts, on account of their inertia, tend to 
move in straight lines, tangent to their respective cir- 
cles, and thus leave the rest of the body ; and they 
would do so, unless restrained by some force. The 
force which tends to carry the particles off in a tan- 
gent is called the projectile force ; that which holds 
them in is called the centripetal force ; and that com- 
ponent of the projectile force which acts directly 
away from the center is called the centrifugal force. 
All these are frequently called central forces. 

65. Illustrations. — We see an illustration of the 
projectile force when a wheel is revolved, having 
water on its edge. The drops are thrown off in tan- 
gent lines. 

If a ball is whirled by a string, the projectile force 
is prevented from carrying the body away by the 



64. What is the projectile force? the centripetal? the centrifiii 
gal ? What common name is given to them all ? 

65. Illustrate by wheel — by ball and string — by the curve of a 
railroad. 



64 THE EAETH. 

strength of tlie string, which is the centripetal force. 
But the string is strained, and may possibly be 
broken by the centrifugal force, which is a part of 
the projectile force. 

When a train of cars turns a curve, there is a cen- 
trifugal force tending to throw it off from the track 
on the convex side. Hence, the outside rail is laid 
highest, so that the cars may lean in the opposite 
direction. 

66, Loss of Weight on the Earth. — As the earth 
revolves on its axis, all objects upon it are affected 
by the centrifugal force, and lose a little of their 
weight. The loss is greatest at the equator, where 
the motion is swiftest ; but even there it is very 
small, only - 2 -|-g of the whole. At all other places the 
loss of weight is less than this, according as the dis- 
tance from the equator is greater. At the poles there 
is no loss at all. 

There is an additional loss of weight at the equa- 
tor, arising from the oblate form mentioned in the 
next article. The whole loss amounts to T ^ ¥ of the 
weight. Therefore, a body on the equator, which 
would weigh 194 pounds if the earth were a sphere 
and at rest, actually weighs only 193 pounds. 

67, Oblate Form of the Earth. — The centrifugal 
force on the earth produces another effect upon 
all the yielding parts, such as the water of the oceans. 



66. How are bodies on the earth affected by its rotation ? Where 
is loss of weight greatest ? How much is the loss by centrifugal 
force ? In what other way is there a loss ? How great is the whole 
loss? 



OBLATE FORM OE THE EAETH 



65 



They tend to flow away from the poles, and all places 
near the poles, towards the equator, until the water at 
the equator is about 13 miles further from the center 
than the poles are. Thus, the earth, as a whole, is 
not an exact sphere, but is flattened in the polar re- 
gions, and has the form which is called an Oblate 





Fig. 

( 


14. 




/& 


\ WW 


/UrP 


\\\Y\ 


n i 


\ \ \\\ 


Jiiv 


i 


1 
G 1 


Ell 


v\ 


I 1 


I i 




vaVA 


/ rrn 


\w\ \ 


n^z/y 




\\ \ 


■r£z?y 









D 



Spheroid. Fig. 14 will give an idea of the earth's 
form, C and D being the poles, and AEGFB the 
equator. The diameter AB of the equator is about 
26 miles longer than CD, the axis on which the earth 
revolves. If we imagine a sphere constructed on the 
polar diameter of the earth, the difference between 
the sphere and spheroid will be a sort of shell or 
ling, 13 miles thick at the equator, and growing thin- 
ner on every side to the poles. This is sometimes 
called the Equatorial Ring or Belt of the earth, and it 



67. What is the earth's form? 
equatorial belt ? 



Why ? What is meant by the 



66 



THE EARTH 



produces sensible effects on the earth's relations to 
the moon and sun. 

08* Weight and Density of the Earth. — The weight 
of the whole earth has been found, by comparing its 
attraction with the attraction of a mountain of given 
Fig. 15. 




size. Thus, if the mountain M exerted no attraction, 
the plumb-lines AB and CD would hang towards the 
center of the earth. But if the mountain alone 
attracted them, they would be drawn directly towards 
the center of gravity of the mountain. But since the 
earth and the mountain both attract, they hang a 
little sideways towards the mountain, as in the dotted 
lines. By carefully measuring the deviation of the 
plumb-lines, it may be learned how much greater the 



68. Describe the mode of finding the weight of the whole earth. 
How great is it ? What is its density, or specific gravity ? 



ROTATION OF THE EARTH. 67 

earth's attraction is than that of the mountain. The 
weight of the earth is about 6,000,000,000,000,000,- 
000,000 tons. 

The size and weight of the earth being both known, 
its density, or specific gravity, is easily found. It is 
expressed by the number 5.67 ; that is, it weighs 5.67 
times as much as the same bulk of water. 

09* Proofs that the Earth Revolves on its Axis, 
The early belief of all people is that the earth is im- 
movable, and that the heavenly bodies revolve about 
it. It is only a few centuries since the wisest philos- 
ophers began to teach that the earth itself revolves. 
But there are several independent proofs that the 
earth really revolves once round every day. 

1. This is the only reasonable way of explaining 
the fact that all the millions of fixed stars, at various 
and immense distances from us, in large and in small 
circles of the sphere, perform their apparent revolu- 
tions about us in precisely the same length of time, viz., 
one sidereal day. 

2. Without supposing the earth to rotate on its 
axis, we cannot account for the oblate form of the 
waters of the ocean. Whatever form the solid parts 
might have, the movable portion would be spherical, 
if the earth were at rest. Moreover, the degree of 
oblateness is exactly that which is required on a 
sphere having the diameter and mass of the earth, if 
it be supposed to rotate once in 24 hours. 



69. Did ancient philosophers believe that the earth revolves? 
What is the first proof that it does ? the second ? the third ? the 
fourth ? the fifth ? the' sixth 1 



68 THE EARTH. 

3. The weight of a body at the equator, compared 
with that at the poles, is too small to be wholly ac- 
counted for by increased distance. Centrifugal force, 
arising from rotation, can alone explain the remain- 
ing difference. 

4. A body dropped from a great height strikes/wr- 
tlier east than the vertical line in which it began to 
fall. If the earth rotates, the top of a tower moves 
faster than the base ; and, therefore, a body let fall 
from the top, retaining the eastward motion of that 
point, will strike further east -than the base. At the 
equator, this distance would be near 2 inches for a 
fall of 500 feet. Numerous experiments on the fall of 
bodies through great distances have been very care- 
fully made by different individuals, and in different 
latitudes ; and they all concur in proving that a body 
in falling deviates from a vertical line toward the 
east. 

5. It is also proved by FoucauWs pendulum experi- 
ment If a very long pendulum be set vibrating north 
and south, it will slowly change to the northeast and 
southwest, thus showing its tendency to preserve, as 
nearly as possible, the original direction of its vibra- 
tion in space. 

6. The precession of the equinoxes can be explained 
only on the supposition that the earth rotates on an 
axis. 



CHAPTEE VI. 

THE SUN — SOLAE SPOTS— CONDITION OF THE SUN'S 
SUEEACE — THE ZODIACAL LIGHT. 

70* The Form of the Sun. — As the sun revolves 
on an axis, the centrifugal force must produce some 
oblateness. It is, however, too slight to be perceived, 
because the velocity of rotation is small, and the 
force of attraction very great. Hence, the appear- 
ance of the sun is that of a perfect sphere. 

71» Tlie Sun's Distance and Size.— The horizontal 
parallax of the son is so small that there is much dif- 
ficulty in measuring it accurately. According to the 
best determinations, it is about 8.6", from which it is 
calculated that the earth's distance from the sun is a 
little more than 95,000,000 miles. 

The distance of the sun being found, and its appa- 
rent breadth being measured, it is easy to compute its 
diameter. This is found to be 887,000 miles, which is 
112 times as great as the diameter of the earth. In 



70. What appears to be tiie form of the sun ? What is its real 
form ? Why does it not appear so ? 

71 . What is the sun's horizontal parallax ? Is it easily found ? 
What is our distance from the sun ? What is the sun's diameter ? 
Compare it with the earth. Compare the sun's and the earth's bulk. 



70 THE SUN. 

bulk, therefore, the sun is 1,400,000 times as large as 
the earth. 

72o The Sun's Mass, and Strength of Gravity, — In 

respect to quantity of matter, the sun does not ex- 
ceed the earth nearly as much as in size ; for while its 
volume is 1,400,000 times as great as that of the earth, 
its mass is only 355,000 times as great as the mass of 
the earth. It follows that its density is only one-fourth 
as great as the earth's density. 

The strength of gravity on the sun is 28 times 
as great as it is on the earth ; so that, what weighs 
100 pounds here, if transported to the sun, would 
weigh 2,800 pounds; and a body there would fall 
through 450 feet in the first second of its descent, 
while on the earth it falls only 16 feet. 

73. Diurnal notation of the Sun. — By means of 
spots on the sun, it is found that it revolves on its 
axis in about 25 days, from west to east, nearly in the 
same plane in which the earth revolves about the sun. 
After a spot has presented itself on the edge of the 
sun's disk, it occupies almost two weeks in going 
across, and then is out of sight as much longer, re- 
appearing in the same place as at first, in 27J- days. 
If the earth were at rest, then 27 J- days would be the 
period of the sun's rotation on its axis ; but since the 
earth revolves about the sun in the same direction, it 
requires more than one revolution of the sun to bring 



72. Compare them in respect to mass. Which is the most dense ? 
How many times ? What is the strength of gravity at the sun ? 

73. How is it found that the sun revolves on its axis ? In what 
time, and in what direction, does it revolve? What is the appa- 



SOLAE SPOTS, 



71 



the spot again to the edge. Suppose the earth at rest 
at the point E (Fig. 16). Then a spot coming into 



Fig. 16. 




view at A would go round through B, D, and H, to A 
again, when it would reappear. But while it goes 
round, the earth in fact advances in its orbit from E 
to F. The edge of the sun's disk is changed to B, 
and the spot mast move so much further before it 
comes in sight again. As it requires about tivo days 
to go over AB, the time of one revolution of the sun 
on its axis is a little more than 25 days. 

74. Appearance of the Solar Spots. — Nearly every 
spot on the sun consists of two parts — a black center 
of irregular form, called the nucleus, and a surround- 
ing part of lighter shade, called the umbra (Fig. 17). 
These parts are distinct, and do not shade into each 
other. The spots not only move across the disk, but 



rent time of revolution ? Describe the cause of the difference, by 
Fig. 16. 



72 



THE SUN. 
Fig. 17. 




# 



July 9 " 



W 



1844. 



July 11 



change their form and appearance from day to day. 
Sometimes a large spot divides into two or more, 
smaller ones ; and, again, a group unites into one or 
two larger spots. A spot sometimes diminishes and 
disappears, first the nucleus, then the umbra. The 
reverse also happens; a spot is seen in the midst 
of the disk, where there was none the day before. 
Though only a few are commonly in sight at once, yet 
in some instances they have been counted by tens, 
and even hundreds. Yery rarely a spot is so large 
as to be seen by the naked eye. They do not cross 
all parts of the disk, but appear chiefly in two zones, 
one on each side of the equator, from 10° to 35° of 
latitude, as shown by the dotted lines in Fig. 17. 



74. Describe a solar spot. What is the nucleus ? the umbra ? 
State what changes the spots undergo. What parts of the disk do 
they pass across ? 



THE ZODIACAL LIGHT. 73 

The same figure exhibits the change which took place 
in a group of spots in the course of two days. 

7&. The Nature of the Spots. — From the changes 
which the spots undergo in passing near the edge of 
the disc, it is found that they are cavities in the lumi- 
nous atmosphere of the sun, the nucleus being deeper 
than the umbra which surrounds it. Sir William 
Herschel proposed the theory that an atmosphere of 
flaming gas forms the outer surface of the sun, having 
a less luminous stratum beneath, while lower down is 
the liquid or solid surface of the sun, which is still 
darker. When an opening is rent in the outer 
stratum, we look in upon the second stratum, and this 
forms the umbra of a spot» And, supposing a smaller 
rent to exist in that, we are able to see the more 
dense portion below, as the nucleus of the spot. Sir 
John Herschel has suggested that these openings, 
one below the other, may be occasioned by rotating 
storms in the solar atmosphere, resembling some 
which take place on the earth. 

76* The Zodiacal Light* — This name is given to a 
faint, ill-defined light, extending along the zodiac, 
either in the west, after sunset, or in the east, before 
sunrise. It so much resembles the twilight that it is 
not ordinarily noticed, because it appears as a mere 
upward extension of it. It is projected on the sky as 
a triangle, inclined to the horizon at the same angle 
as the ecliptic (Fig. 18). In the evening, it is best seen 



75. What is the nature of the spots ? What is Sir William Her- 
Bchel's theory ? 

4 



74 



THE SUN. 



at the season when the ecliptic is most nearly perpen- 
dicular to the horizon, after twilight has ceased. It 
is, therefore, most conspicuous, at evening, in the 
month of February. When the air is clear, and there 

Fig. 18 




is no moon, it is visible till after 9 o'clock. For a like 
reason, the best time for seeing it before morning twi- 
light is the month of October. The apparent extent 
of it, both in breadth and height, is much increased 
by indirect vision. 



76. Describe the zodiacal light. When does it appear in the 
morning? When in the evening? 



CHAPTEE VII. 

GEAVTTATTON — KEPLEE'S LAWS — MOTION LN AN ELLIPTICAL 
OEBIT — PEECESSION OE THE EQUINOXES. 

77 o Gravitation. — AH portions oi matter in the 
universe show a tendency towards each other. This 
tendency is called gravity or gravitation. It is by this 
force that bodies fall to the earth, when left at rest in 
the air, or when thrown in any direction. And it is 
discovered that the same force causes the moon to go 
round the earth, and the planets to go round the sun, 
instead of moving off in straight lines, as they would 
do if there were no such force as gravitation. 

78. First Laiv of Gravitation. — When the distance 
is the same, gravity varies as the quantity of matter. 
Bodies fall as swiftly as they do, because the earth 
contains so great a quantity of matter ; and if it con- 
tained more or less, bodies would fall faster or slower 
in the same proportion. So, also, bodies fall toward 
the earth, instead of falling toward a mountain, be- 
cause the earth contains vastly more matter than the 
mountain. 

Again, we see that gravity varies as the quantity of 



77. What is gravitation ? Where do we observe its operations 

78. What is the first, law of gravitation ? Give the proofs. 



76 GKAVITATION. 

matter, in the fact that the weight of a body increases 
as the quantity of matter in it ; for weight is only 
another name for strength of gravity. 

79. Second Law of Gravitation. — When the quan- 
tity of matter is the same, gravity varies inversely as 
the square of the distance. Hence, if the distance is 
twice as great, gravity is four times less ; if three times 
as great, it is nine times less, and so on. It can be 
demonstrated that this must be the law of gravitation 
in regard to distance, in order that a planet may de- 
scribe an ellipse about the sun, or a satellite about a 
planet, while the central body is situated in the focus. 

80. Kepler's Laws. — From the observed motions 
of the planets about the sun, Kepler deduced the 
three following laws, which are applicable to all 
bodies revolving about a central body. Though Kep- 
ler discovered them as facts in the solar system, they 
were afterwards proved by Newton to be necessarily 
involved in the laws of inertia and gravitation : 

81. (1.) The Areas Described about the Sun by the 
Madias Vector vary as the Times of Describing Them. 

Of course, if equal times are spent, the areas passed 
over are also equal. This is illustrated by a reference 
to Fig. 13. If the sun is at E, and a planet describes 
the orbit aemt, and passes over ah, be, cd, &c, in equal 
times, then the areas dEb, bEc, cEd, &c, are equal. 



79. The second law ? Illustrate by numbers. 

80. Who proved the truth of Kepler's laws mathematically? 
Why are the following laws called Kepler's laws? 

81. State the first law of Kepler. Illustrate by Fig. 13. 



OEBITS OF THE PLANETS. 



77 



This implies that the planet moves fastest when it 
is nearest the central body ; for there the areas are 
shortest, and need to be widest. The velocity is, 
therefore, greatest at a, the perihelion, and least at 
m, the aphelion. 

82, (2,) TJie Orbit of each Planet is an Ellipse, the 
Sun being in one Focus. — Thus, ACBD may represent 
the orbit of a planet, the sun being at E or F, which 
are the two foci. If the foci are nearer the center, the 




ellipse approaches more nearly to the form of a cir- 
cle, in which case it is said to be less eccentric. But 
a more eccentric ellipse is one whose foci are further 
from the center. The figure is then narrower, and 
differs more from a circle. The orbits of the comets 
are generally very eccentric, while those of the planets 



82. State the second law. Where is the sun in a planet's orbit ? 
What is the eccentricity of an orbit? Are the orbits of the planets 
very eccentric ? 



78 GEAVXTATION. 

have very little eccentricity, and, if correctly repre- 
sented, could not be distinguished from circles. 

83. (3.) Tlie Squares of the Periodic Times vary 
as the Cubes of the Mean Distances. — The periodic 
time is the time occupied by a planet in making a 
complete revolution. And, according to this third 
law, the times increase faster than the distances ; for 
the distances must be raised to the third power, in 
order to vary as fast as the second power of the times. 
Hence, the further off a planet is from the sun, the 
slower it moves. 

84. Paths of Projectiles. — When a stone is thrown, 
or a ball is fired, its path (if undisturbed by the air) 
is part of an elliptic orbit, one of whose foci is at the 
center of the earth. This ellipse, however, is one of 
extreme eccentricity, and is, therefore, usually called 
a parabola. Making use of the time and distance of 
the moon's revolution, it is calculated, by Kepler's 
third law, that if there were nothing to- obstruct the 
motion of the projectile, it would complete its orbit, 
and return to the place from which it was thrown, in 
about 31 minutes. The perihelion of this orbit would 
be only a few feet beyond the center of the earth. 

85. Effect of Increased Velocity of Projection. 

Suppose that P (Fig. 20) is a point near the earth, 



83. State Kepler's third law. What planets have the swiftest 
motion ? 

84. When a stone is thrown, what is the form of its path ? What 
is it usually called ? Why ? When would it return if uninter- 
rupted ? Which focus is at the earth's center ? 



WHY PLANETS RETURN AND DEPART. 79 

ADE, and that the velocity of projection, in the direc- 
tion PB, is so greatly increased that the projectile 
strikes the earth at D. By a still greater increase of 




velocity it might meet the earth at E. In these cases 
the earth's center would be in the most remote focus 
of the orbit. But if we suppose the velocity so much 
increased that the centrifugal force just equals the 
force of gravity, then the body would describe the 
circular orbit PFG. Any increase of the velocity of 
projection beyond this will again produce an ellipse, 
as PK, whose nearer focus is at the earth's center. 
And we can imagine the velocity increased till the 
ellipse becomes one of extreme eccentricity. 

SG» Why a Planet at Aphelion begins to Return, or 
at Perihelion begins to Depart, — It might be thought 



85. What is the effect of increasing the velocity of projection? 
When will the orbit "become a circle ? What if the velocity is still 
more increased ? 



80 



GRAVITATION 



that a planet at its aphelion, C (Fig. 21), being less 
attracted toward the sun than at any other point, 
would continue to withdraw, instead of commencing 
to return ; and that when at its perihelion, G, being 
more attracted than elsewhere, it would continue to 
approach till it falls to the sun. The reason why a 
planet begins to return after reaching the aphelion is 
to be found in its diminished velocity. As the planet 




recedes through H, K, and A, the centripetal force 
toward S draws it back, and causes continual retard- 
ation, till at C the velocity is so much diminished that 
the attraction of S, though less than elsewhere, is 
still sufficient to curve the path so that it falls within 
a circle about the centre S, and the planet begins to 
approach the sun. 
Again, as the planet passes through D, E, and F, 



86. Explain by Fig. 21 why a planet returns from aphelion, or 
departs from perihelion. 



PEECESSION OF EQUINOXES. 81 

the attraction toward S partly conspires with its iner- 
tia, and it is continually accelerated, till, at Gr, its 
velocity has become so great that its path strikes 
outside of a circle about the center S, and it begins 
again to depart as before. 

87* Precession of Equinoxes Described, — The points 
in which the equator intersects the ecliptic on the 
celestial sphere are not stationary, but have a slow 
retrograde movement ; that is, they revolve from east 
to west. The sun, therefore, in its annual progress 
eastward, crosses the equator each year a little fur- 
ther west than it did the year previous. This motion 
is called the Precession of the Equinoxes. These points 
move about 50 J" in a year. At this rate, it will re- 
quire 25,800 years to make a complete circuit of the 
heavens. 

88* Signs of the Ecliptic Displaced from the Signs 
of the Zodiac. — The want of coincidence between the 
signs of the ecliptic and the signs of the zodiac was 
noticed (Art. 41). They coincided at the time the 
division was made, about 2,000 years ago ; and the 
precession, during this period, has moved the equi- 
noxes backward 2,000 x 50J" = 28°, nearly. Hence, 
Aries, of the zodiac, almost coincides with Taurus, of 
the ecliptic ; Taurus, of the zodiac, with Gemini, of 
the ecliptic, &c. 



87. What is meant by the precession of equinoxes? How fast 
do they recede ? 

88. What effect has precession produced on the position of the 
signs of the ecliptic ? How much are they now displaced? 



82 GBAVITATION. 

89* Motion of the North and South Poles. — Con- 
sidering the plane of the ecliptic as fixed, its poles, of 
course, occupy fixed positions among the stars. But 
this is not true of the poles of the equator. Their 
distance from the poles of the ecliptic is equal to the 
obliquity of the two circles ; that is, 23° 27'. As this 
angle remains nearly constant, and the points of in- 
tersection move around westward, the poles of the 
equator must likewise move round those of the eclip- 
tic in the same direction, and occupy the same period, 
25,800 years, in completing their revolution. The 
north pole of the equator is now near the star in Ursa 
Minor known as the pole-star. According to the ear- 
liest catalogues, the pole was 12° distant from the 
pole-star. It is now somewhat more than 1° distant, 
and will, at the nearest, pass within J° of it. In 
about 13,000 years the pole will be on the opposite 
side of the pole of the ecliptic, near the bright star 
Alpha Lyrse, which will then be the pole-star. 

90o Cause of Precession. — The precession of the 
equinoxes is a disturbance produced by the sun's and 
moon's attraction upon the equatorial ring of the 
earth. The sun being always in the plane of the 
ecliptic, and the moon always near it, both bodies act 
upon the equatorial ring to tip it into the same plane. 
This action, in connection with the inertia of the earth 
as it revolves on its axis, causes the equinoxes to 
move backward. 



89. What is the effect on the poles of the equator ? What is 
said respecting the pole-star ? 

90. Explain how precession i3 caused. 



TROPICAL AND SIDEREAL YEAR. 83 

91> The Tropical and Sidereal Year, — Tlie fact 
of precession shows that the year has two different 
values, according as we reckon from a star or from an 
equinox. Hence, the Sidereal Year is defined to be 
the period occupied by the sun in passing eastward 
around the heavens from a star to the same star 
again ; and the Tropical Tear, the time of passing 
around from one equinox to the same equinox again 
(Art. 61). vAs the equinox moves westward, the sun 
reaches it sooner than if it were stationary, and thus 
makes the tropical year shorter than the sidereal, 
by the time required to pass over 50J", which is 20m. 
22.9s. As the tropical year is 365c?. 5k 4.8m. 46.155. 
(Art. 61), the sidereal year, therefore, is 365d. 6h. 

9771. 9s. 

Though the sidereal year is the true period of the 
earth's revolution about the sun, yet the tropical year 
possesses by far the greatest interest, because it is 
the period in which the seasons are completed. 



91. What two kinds of year are described ? "Why are there two? 
Which is the true period of the earth's revolution ? 



CHAPTEE VIII. 

THE MOON— ITS INVOLUTIONS— ITS PHASES — THE 
CONDITION OF ITS SUKFACE. 

02, Distance and Dimensions of the Moon* — The 

moon is a satellite of the earth, revolving about it 
within a comparatively small distance, and accom- 
panying it in its orbit around the sun. The mean 
horizontal parallax of the moon at the earth's equator 
being 57' 5", its mean distance is found to be 238,650 
miles. As its apparent diameter is 31' 6", its real 
diameter must be 2,161 miles. Therefore, the surface 
of the moon is 13 times less, and its volume 49 times 
less, than the surface and volume of the earth. But 
in respect to mass, the moon is 80 times less than the 
earth. 

93. Revolution about the Earth. — The slightest 
attention to the position of the moon, from night to 
night, shows that it moves eastward, among the stars, 
several degrees every day. If the instruments of the 
observatory be employed to measure its right ascen- 



92. What is the moon's parallax? its distance from the earth? 
its diameter ? Compare its surface and volume with the earth s ; 
also its mass. 

93. How does the moon move in relation to the earth ? 



Telescopic view of the Moon. 




Telescopic view of the Moon when five days old. 



THE NODES. 85 

sion and declination, it is ascertained that the moon 
describes nearly a great circle, inclined about 5° to 
the ecliptic, and occupies 27.32 days in returning to 
the same place among the stars. 

94. Months. — The period just mentioned, in which 
the moon makes a revolution from a star to the same 
star again, is called the Sidereal Month. The time 
occupied in making a revolution relatively to the sun, 
instead of a star, is called a Synodical Month. This 
is more than two days longer than the sidereal 
month ; for the moon's daily progress is about 13°; 
and during the 27 days of its revolution, the sun, at 
the rate of 1° per day, will advance 27°, requiring 
more than two additional days for the moon to over- 
take it. 

The mean length of the synodical month is 29.53 
days. 

95. Nodes. — The points where the moon's path 
cuts the circle of the ecliptic are called the moon's 
nodes. The ascending node is the one through which 
the moon passes from the south to the north side of 
the ecliptic ; the other, 180° from it, is called the de- 
scending node. 

96. The Moon's Positions in Relation to the Sun. 

The moon is said to be in Conjunction with the sun, 
when both bodies have the same longitude ; in Oppo- 
sition, when their longitudes differ by 180°. The con- 



94. What kinds of month are described ? Explain them. 

95. Name and describe the nodes. 



86 THE MOON. 

junction and opposition are called by the common 
name of Syzygies. 

When the longitude of the moon is 90°, or 270° 
greater than that of the sun, it is said to be in Quad- 
rature. 

The points midway between syzygies and quadra- 
tures are called Octants. 

The period in which the moon passes from any one 
of these points to the same point again (that is, a 
synodical month), is also called a Lunation. 

07* Form of the Moon's Orbit. — It is ascertained 
by the same method as was described (Art. 51), that 
the moon's orbit is an ellipse, one of whose foci is at 
the earth. But its eccentricity is 4J times greater 
than that of the earth's orbit. 

The point of the moon's orbit nearest the earth is 
called the Perigee; the most distant point, the Apogee. 

08* T7ie Moon's Diurnal Motion. — The moon not 
only revolves about the earth, but also on its own 
axis, in the same length of time ; that is, once in 27.32 
days ; and its axis is nearly perpendicular to the 
plane of its orbit. This rotation is indicated by the 
fact that the same side of the moon is always pre- 
sented toward the earth. If it should pass around 
the earth, and not turn upon an axis, it would obvi- 



96. Name and describe the several positions of the moon in rela- 
tion to the sun. 

97. What is the shape of the moon's orbit ? What is apogee ? 
What is perigee ? 

98. What other motion has the moon 1 Do we see all sides of the 
moon? 



THE MOON'S LIBEATIONS. 87 

ously present all sides to us in the course of each 
revolution. 

. But though it keeps the same side toward the 
earth, it presents all sides to the sun once in each 
synodical month. Therefore, the days and nights on 
the moon are nearly 30 (29.53) times the length of 
those on the earth. 

99* The Moon's Librations. — Though the same 
side of the moon is turned to us on the whole, yet 
there are slight apparent oscillations, by which nar- 
row portions of the other hemisphere alternately 
come into view. These are called Librations. They 
are of three kinds — the libration in longitude, the 
libration in latitude, and the diurnal libration. 

By the libration in longitude, we see a little way 
round upon the back side, first on the eastern edge, 
and then on the western. This arises from the un- 
equal velocity of the moon in its elliptical orbit. 

By the libration in latitude, we at one time see a 
little beyond the moon's north pole, then beyond its 
south pole. This is because the moon's axis is not 
exactly perpendicular to the plane of its orbit. 
Both these librations are completed in one sidereal 
month. 

By the diurnal libration, we see a little beyond the 
moon's western limb at its rising, and a little beyond 
its eastern limb at setting; on account of our being 
elevated 4,000 miles above the earth's center. 



99. Do we see any of the back side ? In how many ways ? De- 
scribe the libration of longitude — the libration of latitude — the 
diurnal libration. 



88 THE MOON. 

100. TJie 3Ioon's Revolution about the Sun. — While 
the moon revolves about the earth, the earth revolves 
about the sun, at a distance 400 times as great. 
Therefore the moon really has a third revolution; 
namely, that in company with the earth around the 
sun. And this is far greater than its other revolu- 
tions, which have been described. Since the moon 
goes round the earth, its path jnust lie outside of the 
earth's orbit one-half of the time, and the other half 
within it. The path is, therefore, a waving line, which 
crosses the earth's path 25 times in a year. But the 
moon's orbit is so small, and the earth's motion so 
swift, that the waves are very long and narrow, and 
everywhere concave toward the sun. 

101. Phases of the Moon. — The moon is not self- 
luminous, and is seen only as it reflects to us the light 
which falls upon it. The several forms which the 
part illuminated by the sun presents to our view, are 
called Phases. 

The Circle of Illumination, or the Terminator, is the 
circle which separates the hemisphere enlightened by 
the sun from the dark hemisphere, and is perpendicu- 
lar to the sun's rays which fall on the moon. The 
Circle of tlie Disk is that which separates the hemi- 
sphere turned toward the earth from the opposite 
one, and is perpendicular to our line of vision. The 
phase depends on the size of the angle formed at the 
moon, between the solar ray and our visual line. 

Let the earth be at E (Fig. 22), and the moon in 



100. What third revolution lias the moon ? What kind of a path 
is it ? How can it be everywhere concave toward the sun ? 



PHASES OF THE MOON. 



89 



several positions, A, B, &c., and let the lines AS, BS, 
&c, be directed toward the sun. At A, the moon is 
in conjunction, and wholly invisible — this is called 
Neiv Moon; and the angle SAE, between the solar ray 
and visual ray, is 180°. From A to C (as at B), the 
phase is called Crescent; and the angle SBE is obtuse. 
The First Quarter occurs at C, the quadrature, where 
SCE is a right angle. From to F (as at D), the 

Fig. 22. 



O 




phase is called Gibbous. In this phase, the angle SDE 
is always acute. At F, the moon is in opposition, 
and wholly illuminated. This is called Full Moon. 
The angle SFE is 0°. From F to A, the phases are 
repeated in reverse order, the Last Quarter being at 
H. The outer figures at B, C, &c, show the corres- 
ponding phase. 



101. What is meant by phases' 
using Fig. 22. 



Explain the several phases, 



90 THEMOON. 

102. Moon Munning High or JLoiv. — It is gener- 
ally observed that, at a given age of the moon, for 
instance, at the full, its meridian altitude is very dif- 
ferent at different seasons of the year ; that is, that 
the full moon runs high at some seasons, and low 
at others. This is readily explained by noticing the 
moon's relations to the sun. As the moon's path is 
everywhere near the ecliptic, the new moon will cul- 
minate at a high point when the sun does ; that is, in 
the summer. But, in the same season, the full moon, 
being opposite to the sun, will culminate low. On the 
contrary, when the sun is in the most southern part of 
the ecliptic, and culminates low, as is the case in win- 
ter, the new moon will do so likewise ; but the full 
moon will culminate at a high point. In the polar 
winter, therefore, when the sun is absent for months, 
the moon, whenever near the full, circulates round 
the sky without setting. 

103. The Harvest Moon, — This name is given to 
the full moon which occurs nearest to the autumnal 
equinox, September 22d, and which rises from evening 
to evening with a less interval of time than the full 
moon of any other season. 

The sun being at the autumnal equinox, the moon 
is near the vernal equinox, and at sunset the southern 
half of the ecliptic is above the horizon, and makes 
the smallest possible angle with it. It is this small 



If 2. When does the full moon run high ? when low ? Show why. 
Where does the full moon shine all the time for many days with- 
out setting? 

103. Which moon is called harvest moon ? Explain the small 
difference in the time of rising. Why not noticed every month ? 



THE MOON'S SUE3TACE. 91 

angle, made by the ecliptic, and, therefore, by the 
moon's orbit with the horizon, which causes the small 
interval in the time of the moon's rising from one 
evening to another ; for, as the moon advances 13° 
each day in its orbit, this arc is so^oblique to the 
horizon, that its two extremities rise with only a few 

minutes' difference of time ; but the 'place of rising 

moves rapidly northward. 

The harvest moon attracts most attention in high 

latitudes, where the angle between the ecliptic and 

horizon is smaller, and, therefore, the intervals of time 

are less. 
The moon passes the vernal equinox every month, 

and, therefore, rises with the same small intervals. 

But when the moon is not full at the same time, the 

circumstance is unnoticed. 

104. Inequalities of the Moon's Surface. — These 
are clearly revealed by the changing direction of the 
sun's rays. As the terminator advances over the disc, 
the light strikes the highest peaks, which appear as 
bright points a little way upon the dark part of the 
moon. After the terminator has passed over them, 
they project shadows away from the sun, which cor- 
respond to the apparent shape of the elevations, and 
grow shorter as the rays fall more nearly vertical. 
And again, in the waning of the moon, the shadows 
are cast in the opposite direction, lengthening until 
the dark part of the disc reaches them, and the sum- 
mits once more become isolated bright points, and 
then disappear. 



104. How do we know the moon is mountainous ? 



92 THE MOON. 

105. Forms of Valleys. — The most striking char- 
acteristic of the moon's surface is its numerous circu- 
lar valleys. The smaller and more regular ones are 
of all sizes, from one or two miles in diameter up to 
sixty miles. These are numbered by hundreds. The 
mountain ridge which surrounds one of these cavities 
is a ring, very steep and precipitous on the inner 
side ; but externally it falls off by a rugged but grad- 
ual slope. These ridges are called Ring Mountains. 
In the central part of the cavity are generally one or 
more steep, conical mountains. 

There is another class of larger but less regular 
cavities, sometimes called Bulwark Plains. Their 
diameters are often more than one hundred miles. 
These are also surrounded by rough mountain masses 
arranged in a circle. Over these plains are sparsely 
scattered small conical and ring mountains. 

There are still larger tracts, more level than the 
general lunar surface, and of a darkish hue, which 
still retain the name of seas, formerly given them, 
though they are covered with permanent inequalities, 
and show no signs of being fluid. 

At the time of full moon, there are seen around 
a few of the principal ring mountains a great many 
luminous stripes, radiating in straight lines, and ex- 
tending, in some cases, hundreds of miles. These are 
sometimes called Lava Lines. 

10G» Volcanic Appearance of the Moon, — Every 
part of the moon's surface has the appearance of 



105. Describe the valleys. What is meant by the seas ? What 
appearance at full moon ? 



NO ATMOSPHERE OE VAPOR. 93 

rocky hardness. The interior slopes of the ring 
mountains are steep, rough, and angular. The coni- 
cal peaks within them appear like isolated rocks, 
resembling the needles of the Alps. The surface 
nowhere gives indication of having been softened 
down by the action of water. The circular cavities, 
with steep and rugged sides, appear like vast craters, 
and the mountains within them like volcanic cones, 
more recently thrown up. Nearly every part of the 
hemisphere presented to our view exhibits these indi- 
cations of former volcanic action, on a scale far be- 
yond anything on the earth. But there is no evidence 
of volcanic action at present. % 

107 • Height of the Lunar Mountains. — The height 
of a mountain on the moon can be determined either 
by observing how far from the terminator it is when 
the sunlight just touches its summit, or by measuring 
the length of its shadow. The highest of the lunar 
mountains are from three to four and a half miles 
high. "While the diameter of the moon is not much 
more than one-fourth as great as the earth's diame- 
ter, its mountains are nearly equal in height to the 
mountains of the earth. 

10S» Wo Atmosphere or Vapor. — If any kind of 
atmosphere were spread over the disk of the moon, it 
would reflect the sun's light so strongly as to dim the 
features of the solid surface. Nothing of the kind is 
ever perceived. No terrestrial objects, however near, 



106. What are tlie proofs of past volcanic action ? 

107. How is the height of lunar mountains found ? How high 
are they ? 



94 THE MOON. 

ever exhibit greater sharpness of outline than the in- 
equalities of the moon ; and they never vary in this 
respect, except in a manner which is obviously occa- 
sioned by our own atmosphere. 

A still better proof that there is no atmosphere on 
the moon is the fact that when its edge passes be- 
tween us and the stars, they are not dimmed, nor 
their position disturbed in the least. 

100. Changes of Temperature on the Moon. — The 

moon's equator makes an angle of only 1J° with the 
ecliptic, and, therefore, experiences no perceptible 
change of seasons ; but its diurnal rotation is so slow 
that the extremes of heat and cold during each day 
are excessive. A place on the moon is exposed to the 
full power of the sun's rays for about two weeks, and 
then is for as long a time turned away from the sun, 
without clouds, or even air, to prevent the free radia- 
tion of heat. 

110. View of the Earth from the Moon, 

1. As to Magnitude. — The apparent dimensions of 
the two bodies, as seen one from the other, are pro- 
portional to their real dimensions. Hence, in diame- 
ter, the earth, as seen from the moon, is 3f times as 
large as the moon, viewed from the earth, and in area 
is about 13 times as large. 

2. As to Phase. — It is obvious, from Fig. 22, that 
when the full moon is presented to the earth, the 
earth's dark side is toward the moon, and the reverse. 



108. Has the moon an atmosphere ? How proved ? 

109. What is said of changes of temperature on the moon ? 



VIEW OF THE EAETH. 95 

Also, that when we see the gibbous phases of the 
moon, a spectator on the moon would see crescent 
phases of the earth ; for the angle SED or SEG 
would then be obtuse. In like manner, the relative 
phases are in every case supplementary to each 
other. This relation explains the well-known fact 
that near the time of new moon, the part of the moon 
not directly enlightened by the sun is distinctly visi- 
ble. It is then illuminated indirectly by the earth, 
which is nearly full, as seen from the moon, and re- 
flects a strong light upon it. 

For the same reason, the moon can be faintly seen 
in a total solar eclipse. 

3. As to Position in the SJcy.—The earth, seen from 
the moon, has no apparent diurnal rotation, as all 
other heavenly bodies have, but. remains nearly fixed 
in the same part of the sky. This is owing to the 
fact that the moon's monthly motion and its diurnal 
motion are at the same rate in the same direction, so 
that one apparent motion of the earth neutralizes the 
other. Hence, a spectator occupying the middle of 
the moon's disk sees the earth perpetually near his 
zenith. Another, at the edge of the disk, sees it 
always near the same point of the horizon. 

The first and second librations of the moon, since 
they vary the spectator's position a little in relation 
to the disk, merely cause small oscillations of the 
earth's place in the sky. 

4 As to Surface. — The earth, by its rotation, pre- 
sents all its parts to the view of the nearer hemi- 



110. State how the earth appears, seen from the moon — as to 
magnitude — as to phase — as to position in the sky — as to surface. 



96 THE MOON. 

sphere of the moon once in 25 hours. To the other 
hemisphere it never appears at all. 

On account of its nearness, and its great size, we 
might suppose that the geographical features of the 
earth would be very conspicuous to a spectator on 
the moon, and that the nature of its surface in nearly 
all respects could be thoroughly observed. But the 
deep and dense atmosphere of the earth would reflect 
an intense light, so as probably to render the inequal- 
ities of the terrestrial surface nearly invisible ; and 
whenever clouds prevail over a country, that portion 
of the earth's surface would, of course, be entirely 
hidden from view. 



CHAPTEE IX. 

ECLIPSES OF THE MOON AND SUN. 

1 11, General Relations in Eclipses. — The moon is 

eclipsed when it is obscured wholly or in part by the 
earth's shadow. It can occur, therefore, only at op- 
position, or full moon. The sun is eclipsed when it is 
either wholly or partially concealed from view by the 
moon coming between it and the earth. This can 
happen only at conjunction, or new moon. 

If the moon's orbit and the ecliptic were coincident 
planes, there must be an eclipse of the moon at every 
full moon, and an eclipse of the sun at every new 
moon ; for at those times the three bodies would be 
in a straight line. But as the moon's orbit and the 
ecliptic make an angle of 5° with each other, the 
moon generally passes opposition and conjunction so 
far north or south of the sun, that there is no eclipse. 
That an eclipse may occur, the syzygies must happen 
near the line of nodes, so that, as the moon comes 
into conjunction or opposition, some parts of the 
three bodies may be in a straight line. Fig. 23 will 
illustrate this. Let NA be a small portion of the 
ecliptic, and KB, of the moon's orbit. N is the 



111. When is the moon eclipsed ? the sun ? Why are there not 
eclipses every month ? Show by Fig. 23. 



98 ECLIPSES. 

ascending node. If the sun is at N, when the moon 
is in conjunction, the latter will come exactly between 
the sun and the center of the earth, and cause a cen- 
tral eclipse. But if the sun has passed by the node 

Fig. 23. 




to E, when the moon comes to conjunction at F, then 
it will conceal only the north limb of the sun. If the 
sun is still further from the node, as at C or A, then 
the moon will pass by at D or B, without appearing 
to overlap the sun, and no eclipse will occur. 

112. Eclipse Months. — As there are two nodes on 
opposite sides of the heavens, the sun, in its annual 
progress, must pass through both of them every year, 
at intervals of about six months. And as the moon 
comes into the line of syzygies every two weeks, the 
sun will certainly be near enough to a node for one or 
two eclipses, and possibly for three, every six months. 
Thus, the eclipses of any year always occur in clus- 
ters, at opposite seasons. If two or three are in Jan- 
uary, the others are in July. These are called the 



112. How are the eclipses of any year arranged ? Why 



ECLIPSE OF THE MOON 



99 



Node Months of that year. In 1866, for example, the 
node months are parts of March and April, and parts 
of September and October. On account of the retro- 
grade motion of the nodes, the sun passes from a 
node to the same one again in less than a year, so 
that the node months occur earlier each successive 
year perpetually. 

113. Eclipse of the Moon. — When the moon is 
eclipsed, there is nothing interposed to hide it from 
our view ; but it merely falls into the shadow of the 
earth, and is obscured. This obscuration may possi- 
bly continue for several hours. 



Fig. 24. 





The sun being vastly larger than the earth, the 
total shadow of the latter is a cone, as represented in 
Fig. 24, where the cone of the earth's shadow extends 
to the extreme right hand. It is found by calculation 



113. What is the shape of the earth's total phadow? How long 
is it ? Where does the nioon pass it ? What is the penumbra? 



100 ECLIPSES. 

to be nearly 900,000 miles long ; and the moon is so 
near the earth as to go through the broader part of 
the shadow. 

But besides the total shadow, there is a partial 
shadow, called the Penumbra, surrounding the other. 
It has the form of an increasing cone. When the 
moon is eclipsed, it must pass through the penumbra 
before it reaches the total shadow, and again after 
leaving it. In Fig. 24, the moon enters the penumbra 
at a, and finally leaves it at b. 

114. Length of Lunar Eclipses, and Appearance 
of the Moon. — The breadth of the total shadow, 
where the moon passes it, is nearly three times, and 
that of the penumbra nearly five times, the breadth of 
the moon. Now the moon moves over its own breadth 
in about an hour. Hence, when the eclipse is central, 
it continues between five and six hours. The penum- 
bra, however, is so faint that its effect is scarcely no- 
ticeable ; so that the whole apparent duration of a 
central eclipse is only about four hours. 

But even when buried in the total shadow, the 
moon is not invisible, but shines very dimly, appear- 
ing of a dull red color. This is owing to the sun's 
fight which the earth's atmosphere refracts into the 
shadow. Some of the sunlight thus falls on the face 
of the moon all the while it is in eclipse, and renders 
it visible. 

115. Eclipse of the Sun, — An eclipse of the sun is 
of a different character from an eclipse of the moon. 



114. How long can a lunar eclipse last ? How does the moon ap- 
pear in eclipse ? Why ? 



ECLIPSE OE THE SUN. 101 

"When the moon is eclipsed, it is obscured by the 
earth's shadow falling on it. The moon itself is 
affected. But the sun is said to be eclipsed when the 
moon intervenes between it and the earth, and hides 
it from our view. The sun itself suffers no change, 
but we are placed in circumstances which prevent our 
seeing it. The phenomenon would more properly be 
called an Occultation of the sun. 

110. Total Shadow and Penumbra of the Moon. 

The moon's total shadow is a cone of tne same form 
as the earth's ; but its mean length is only about 
232,000 miles, and does not generally quite reach the 
earth. The moon's total shadow is also surrounded 
by a penumbra. These are both represented in Fig. 
24, where the moon at m stretches its total shadow 
nearly to the earth's surface, while the penumbra 
spreads over a large portion of it. "When the moon 
is nearest, and its shadow longest, it reaches so far as 
to be cut off by the earth's surface, and form a dark 
circle, 170 miles in diameter. The penumbra gener- 
ally covers a circle 4,000 miles in diameter, repre- 
sented by cd in the figure. The circle of the penum- 
bra is faintly shaded at the edges, and grows darker 
towards the center, where the dark circle is situated. 

117. Total and Partial Eclipses of the Sun.— When 
the moon's total shadow reaches the earth, and forms 
a dark circle on it, a person within that circle wit- 



115. How does a solar eclipse differ in character from a lunar 
eclipse ? What is the appropriate name ? 

116. State the form and length of the moon's total shadow. How 
much of the earth's surface can it possibly cover ? How much can 
the penumbra cover ? 



102 



ECLIPSES 



nesses a total eclipse of the sun. This is one of the 
most sublime and impressive phenomena of nature. 
The sun is completely hidden from view, though the 
sky may be perfectly clear. The whole heavens have 
something of the appearance of night, and the bright- 
est stars are visible. The chill of evening is also felt, 
and animals retire to their resting places. 

But those who are situated outside of the total 
shadow, and within the penumbra, perceive the sun 
'partially hidden, one side of it being covered up by 
the circular edge of the moon. A partial eclipse of 
the sun usually attracts no great attention, because, 
unless nearly the whole of it is covered, its light is 
not so much diminished as it often is by clouds. 

Fig. 25. 




117. Describe a total eclipse of the sun. What persons see it ? 
And what persons see a partial eclipse ? 



NUMBEE OE ECLIPSES. 103 

118* Annular Eclipse. — When the moon's shadow 
does not reach the earth, those who are in the direc- 
tion of it see a partial eclipse of a very peculiar form. 
The sun is all covered by the moon, except a narrow 
ring around its edge. As the visible part of the sun 
has the form of a ring, this kind of eclipse is called 
Annular. (See Fig. 25.) 

119* Velocity of the Shadow, and Duration of an 

Eclipse. — The moon moves in its orbit at the rate of 
about 2,000 miles in an hour. Therefore its shadow 
crosses the whole breadth of the earth in a little less 
than 4 hours. But since the earth revolves on its 
axis in nearly the same direction, and with one-half 
the same velocity at the equator, the shadow passes 
by a place at the rate of a little more than 1,000 miles 
per hour. Of course, all total and annular eclipses 
are short, the former not more than 8 minutes, and 
the latter not more than 13 minutes ; but the whole 
duration of an eclipse, at a place where it is central, 
may be about 2 hours. 

120, Relative Number of Solar and Lunar Eclipses. 

On the whole earth there are only about two- thirds 
as many eclipses of the moon as of the sun ; but, 
because one is really an eclipse, and the other an 
occultation, eclipses of the moon at a given place are 
more frequent than those of the sun. An eclipse of 



118. What is an annular eclipse ? In what circumstances does it 
occur ? 

119. How swiftly does the shadow move over the earth ? How 
long can a total eclipse continue ? an annular ? a partial ? 

120. Which kind of eclipses occurs most frequently on the whole 
earth ? at any given place ? Explain the reason. 



104 ECLIPSES. 

the moon is visible to all on the hemisphere nearest 
to it, without regard to locality. But an eclipse of 
the sun is not seen at a place, unless the moon's 
shadow falls at that place. 

121. Eclipses at the 3Ioon. — When we witness a 
solar eclipse, a spectator at the moon would notice 
only a small, dimly-defined circular shadow passing 
over the earth's disk. It would be a partial eclipse 
of the earth. 

But when we see a total lunar eclipse, the phenom- 
enon at the moon would be one of great interest, and 
of very strange appearance. A dim red light from 
all parts of the sun's disk is spread over the moon, 
being refracted thither by the earth's atmosphere. 
Hence, a spectator there would see the sun expanded 
out into a thin dull red ring, surrounding the earth, 
and, therefore, having nearly four times the usual 
diameter of the sun's disk. 

122, True Form of SJiadoivs. — It is impossible, 
in ordinary diagrams, to present the shadows of the 
earth and moon in their true proportions. The dis- 
tance of the sun is so very great, compared with its 
diameter, that the shadows are exceedingly slender, 
having a length about 110 times the diameter of the 
base. The earth being represented as in Fig. 24, the 
length of its shadow, if rightly proportioned, ought 
to be more than five feet long. 



121. When we see a solar eclipse, what can be seen at the moon ? 
And what, when we see a total lunar eclipse ? 

122. What is the true form of the shadows of earth and moon ? 
Why not exhibited in diagrams ? 



CHAPTEE X. 

LONGITUDE — TIDES. 

123. Local Time,— Time is reckoned at every place 
from the moment when the sun crosses the meridian 
at either the upper or the lower culmination. This is 
called local time ; for at the same absolute instant, 
the time thus reckoned at any place differs from that 
on every other meridian. 

124:* Connection between Longitude and Local 

Time. — The earth turns uniformly on its axis toward 
the east through 15° every hour. Therefore, a place 
lying eastward of another will have the sun earlier 
on its meridian, and, consequently, in respect to the 
hour of the day, will be in advance of the other at 
the rate of one hour for every 15°. Thus, to a place 
15° east of Greenwich observatory, it is 1 o'clock 
P. M. when it is noon at Greenwich ; and to a place 
15° west of that meridian, it is 11 o'clock A. m. at 
the same instant. Hence, the difference of local 
time at any two places indicates their difference of 
longitude. 



123. What is local time ? 

124. How is it connected with longitude ? Illustrate. 



106 LONGITUDE — TIDES. 

12o, Longitude by the Chronometer. — If a person 
leaves London with a chronometer accurately ad- 
justed to Greenwich time, and travels eastward till he 
finds his own time slower than the local time of the 
place by Hi. 30???., then he knows the place to be 
22° 30' east longitude. For 15° x 1J = 22J . On 
the contrary, if he travels westward, and at length 
finds his time-piece at Qh. 44m., when the local time is 
4/?. 32m. (in other words, that his Greenwich time is 
2/?. 12??2. too fast), then the longitude of the place is 
33° W. In the same manner, the longitudes of any 
two places may be compared with each other. 

For the use of navigators, chronometers are made 
which run with very great accuracy, and may be 
relied on during long voyages. There is always a 
probability, however, that a chronometer may change 
its rate somewhat, when it comes to be transported 
from place to place. It is, therefore, safer, on long 
voyages, to use several chronometers, and employ the 
mean of all their indications. 

126o Longitude by Eclipses of the Moon, and of 
Jupiter's Satellites. — In one respect, these eclipses 
are very favorable for the comparison of longitudes. 
They are distant phenomena, seen at the same abso- 
lute instant by all. Hence, any difference of time in 
the observations at different places is entirely due to 
difference of longitude. 

But in another respect, they are quite unfitted for 



125. How is longitude found by a chronometer ? 

126. How found by eclipses of moon and Jupiter's satellites ? 
What is the advantage, and what the disadvantage of this method ? 



THE LUNAR METHOD. 107 

the purpose. On account of the penumbra, there is 
no definite edge to the shadow which passes over the 
disk, and, consequently, there is great uncertainty as 
to the time of beginning or end of the eclipse. This 
method is but little depended on for accurate results. 

127 • Longitude by a Solar Eclipse, — In both the 
above particulars, a solar eclipse differs from a lunar. 
It is not an event at a distance, seen at once by all, 
but on the earth's surface, happening to one place at 
one instant, and to another place at another. The 
time of beginning or end of a solar eclipse depends 
on the position of the observer. 

On the other hand, the phenomenon is very defi- 
nite, and the moments of immersion and emersion 
of the sun's limb can be quite accurately fixed by 
observation* , 

Occultations of stars by the moon are much more 
frequent than the occultation of the sun; and these 
are phenomena of the same general character, and 
may be used in the same way for finding the longi- 
tude of a place. 

128* Longitude by the Lunar Method. — This is a 
method particularly useful to navigators, because the 
observations are made by the sextant. It consists in 
measuring the angular distance between the moon 
and some conspicuous heavenly body, as the sun, or 
a large planet or star, and then correcting the ob- 



127. How is a solar eclipse favorable, and how -unfavorable, for 
finding longitude ? 

128. What is the lunar method ? 



108 LONGITUDE — TIDES. 

servation for parallax or refraction, so as to have the 
true distance between the bodies, as seen from the 
center of the earth. The observer must also note the 
local time when this measurement is made. 

Having with him the Nautical Almanac, in which 
the distances, as seen from the earth's center, are pre- 
dicted for every day and hour of Greenwich time, he 
looks for the Greenwich time at which the distance 
agrees with the distance as he has obtained it. The 
absolute time is the same ; hence, the difference of 
time shows his longitude from Greenwich. 

The bodies whose angular distances from the moon 
the Nautical Almanac gives for every three hours, 
with proportional numbers for interpolation, are the 
Sun, Venus, Mars, Jupiter, Saturn, and nine bright 
fixed stars. 

129. Longitude by the Telegraph. — Since the in- 
vention of the magnetic telegraph, it has been em- 
ployed to determine the differences of longitude 
between fixed stations on land with a precision which 
was before altogether unattainable. Suppose two 
stations to be connected by the telegraphic line, and 
that there is at each a clock keeping the local time. 
The observers make signals at certain times agreed 
on ; and each notes on his own clock the times of the 
signals given by the other. Electricity moves so 
swiftly, that a signal may be considered as received 
at the same absolute instant in which it is given. 
Hence, the difference of the clocks is merely a dif- 
ference of longitude. 



129. State how the telegraph is used for this purpose. 



AMBIGUITY AS TO DAYS. 109 

130* Change of Days in Circumnavigating the 
Earth* — While a person travels westward, he length- 
ens his days by one hour for every 15°, or 4 minutes 
for every degree, since he moves along with the ap- 
parent diurnal motion of the sun. In traveling east- 
ward, on the contrary, he shortens the days at the 
same rate, by moving in opposition to the sun's daily 
progress. If we suppose him to go westward entirely 
round the earth to the same meridian again, whether 
he takes a longer or a shorter time for the journey, 
he will lengthen the individual days sufficiently to 
make the whole number just one day less than if he 
had remained where he was. The 5th of a month is 
to him the 4th ; and Tuesday, according to his reck- 
oning, is Monday. The reason is obvious ; for during 
his journey, the earth has made a certain number of 
diurnal revolutions from west to east; but he, by 
going round from east to west, has, in respect to him- 
self, diminished that number by one. 

All this is exactly reversed when one goes round 
the globe from west to east. He gains just a day by 
making all the days of his travel a little shorter. It 
is plain that he makes one more diurnal revolution 
from west to east than the earth does. 

Of course, if these two individuals meet at their 
place of starting, they differ from each other just two 
days in their reckoning. 

~L31., Ambiguity as to Days among the Islands of 
the Pacific Ocean, — If an island in the Pacific were 



130. What change of day is there to a person who goes round 
the earth to the east ? to the west ? How will they differ from 
each other ? 



110 LONGITUDE — TIDES. 

settled by navigators, who had gone westward, and 
also by others, who had sailed eastward, the reckoning 
of these two parties would differ by one day. To the 
former, a day will be the first of a month when it is 
the 2d to the latter. It is, in fact, true that there are 
islands lying contiguous to each other which have 
this difference of reckoning. 

If inhabited land extended entirely round the earth, 
it would be necessary to fix arbitrarily on some me- 
ridian on which the change of day should be made. 
For it is impossible that the reckoning of days should 
go on unbroken around the earth. The arbitrary 
meridian would separate between places which differ 
a day from each other ; so that, on the west side of it, 
the time is one day later, both in the month and the 
week, than on the east side. 

132. Definitions Melating to Tides. — The Tides are 
the daily rising and falling of the waters of the ocean. 
When the water, in this dailv oscillation, has reached 
its highest point, it is called High Water; at its lowest 
point, it is called Low Water. Y/hile the water is 
rising, it is called Flood; and while falling, El)b. 

A Lunar Bay is the time between two successive 
culminations of the moon. Its length is about 24 7 ?. 
52m., being nearly an hour longer than a solar day on 
account of the rapid eastward motion of the moon. 
The tides make their revolutions within the lunar 
day. 



131. What difference of days occurs among the islands of the 
Pacific ocean ? 

132. Define the terms in this article. How long is the lunar day ? 



OPPOSITE TIDES. Ill 

Twice in a lunation high water is at a maximum, 
and twice it is at a minimum. The former are called 
Spring Tides ; the latter, Neap Tides. The spring 
tides occur near the time of syzygies ; the neap tides 
near the time of quadratures. 

133* Opposite Tides. — There are two tide-waves 
on opposite sides of the globe, moving around it from 
east to west, and arriving at any place at intervals, 
whose mean value is 12h. 26m., or half a lunar day. 
Since the mean diurnal motion of each of the two 
opposite tides is the same as that of the moon, the 
action of the moon must be regarded as the principal 
cause of the tides. 

134. Form of the Water acted on by the 3Ioon, 

If the earth were covered with water, and no force 
were exerted except gravitation toward the earth 
itself, its form would be exactly spherical, as repre- 
sented in Fig. 26. But if a distant body, as the 
moon, should also attract it, the sphere would be 
changed into a Prolate Spheroid ; that is, into a form 
produced by revolving an ellipse about its major axis. 
Let the moon be in the direction of CE produced, and 
suppose the center of gravity of the nearer half of 
the water, DEF, to be at A, and that of the remote 
half at B, while the center of the earth, as a whole, 
is at 0. Since A is more attracted than C, and C 
more than B, the form of equilibrium must be dis- 
turbed, and some of the water will flow toward E, and 



133. What is meant by opposite tides ? 

134. How would tho moon change the form of the globe if cov- 
ered with water ? Explain by Fig. 26. 



112 



LONGITUDE — TIDES 



oilier parts toward G, till the particles are in equi- 
librio between their unequal tendencies to the moon 
and their gravity on the inclined surface of the 
spheroid. E and G are the highest points of the 




spheroid, and all points on the circle DF (perpen- 
dicular to EG) are the lowest. Every section through 
EG is an ellipse, whose major axis is EG, and whose 
minor axis is equal to DF. The ellipticity of the 
section will obviously depend not only on the strength 
of the moon's attraction, but also on the difference 
between the attractions on the nearer and remoter 
parts. 

In the case of the earth and moon, it is computed 
that the major axis would exceed the minor by 5 feet ; 
that is, the tides would be only 2J feet high, and on 
opposite sides of the earth, one directed toward the 
moon, the other from it. The tide on the side nearest 
the moon is sometimes called the direct tide ; the one 
on the remote side, the opposite tide. 

'135, Tides by the Sun. — The same kind of effect 
is produced by the sun as by the moon. But the dis- 



INERTIA OF WATER. 113 

tance of the sun is so great, that though it attracts 
the earth more than the moon does, yet the difference 
of its attractions on the several parts is less. The 
power of the moon to raise a tide is to that of the 
sun about as 5 to 2. 

ISO. Joint Action of the Sun and 31oon. — At the 

time of conjunction, the moon and sun attract in the 
same direction, and, therefore, the tides are equal to 
the sum of the lunar and solar tides. The same is 
true at opposition, because each body produces two 
tides at once ; and the direct lunar tide coincides with 
the opposite solar tide, and vice versa. These are the 
spring tides which occur at the syzygies. 

At quadratures, each body raises a tide at the ex- 
pense of that raised by the other. For if the moon 
is in the direction of EG produced (Fig. 26), it causes 
high water at E and G, and low water at D and F. 
And if the sun is in the direction of DF produced, it 
causes high water at D and F, and Ioy/ water at E 
and G. As the lunar tides are the highest, E and G 
are the neap tides, made less by this action of the 
sun than if the moon had acted alone. 

137. Effect of the Inertia of Water. — If the moon 
and earth were at rest, the tides would be directed 
exactly to and from the moon. But while the waters 
are flowing toward these points, the moon, by the 
diurnal motion, passes westward, and causes them to 



135. Compare the sun's action with the moon's. 
186. When will the sun and moon conspire in their action? 
When will they counteract each other ? 

137. What is the effect of the inertia of the water ? 



114 



LONGITUDE — TIDES, 



change the places at which they tend to accumulate. 
Thus, even if the waves were unchecked by the shores 
of continents and islands, the summit would be two 
or three hours behind the moon in passing a given 
meridian. 

138. Diurnal inequality. — At a given place, the 
two tides which follow the culmination of the moon 
will vary in height, according to the relation between 
the latitude of the place and the mioon's declination. 

Fig. 27. 




If the moon, M (Fig. 27), is on the equator, it is clear 
that the tides on the equator, EQ,~are greatest, and 
that in other places they are less, as the latitude is 
greater. But the two successive tides at any place 
are equal ; for, by the rotation on NS, the tide at B 
in 12 -J hours will come round to A, and be equal to 
the tide now there. The same is true of the tides C 
and D, or F and G. Hence, when the moon has no 
declination, there is no diurnal inequality. 



138. Describe the diurnal inequality. When will the direct tide 
be greater than the opposite tide? When will the opposite tide be 
the greatest ? 



EFFECT OF COAST; 



115 



But suppose the moon has a northern declination, 
as in Fig. 28. Then the highest points of the tide 
are at A in north latitude, and D in south. At A, 
where the direct tide is large, the opposite tide, now 
at B, will arrive in 12J hours, and will be small. But 
afc 0, this is reversed ; the direct tide is small, and 



Fig. 28. 





the opposite one (now at D, and arriving at C 12J 
hours later), is large. Therefore, when the declina- 
tion and the latitude are both north, or both south, 
the direct tide (that is, the tide which first succeeds 
the upper culmination of the moon) is larger than the 
opposite tide ; but if one is north, and the other 
south, the direct tide is smaller than the opposite 
tide. This difference in the height of the two suc- 
cessive tides is called the diurnal inequality. 



130o Change of Direction and Velocity caused by 

Coasts. — The tide-wave, which would move regularly 
westward around the earth, if it were wholly covered 
by deep water, is exceedingly broken up and changed, 



139. Explain how coasts affect the direction and velocity of tides. 



116 



LONGITUDE — TIDES 



both in direction and velocity, by coasts and shoals. 
Its general direction is westward ; but as it can pass 
the continents only at their southern extremities, it 
bears to the northwest, and then to the north, in the 
Atlantic and Pacific oceans ; and when it enters seas 
or channels, it usually bends its course in the direc- 
tion of their length. 

140. Cotidal Lines. — These are lines drawn on a 
chart of the oceans, showing the position of the sum- 
mit of the tide-wave for each hour of a day. Such a 
system of lines expresses to the eye the direction and 
velocity of' the tide at all places. Thus, on the open 

Fig. 




ocean, the figures 1, 2, 3, 4 (Fig. 29), show the situa- 
tion of one and the same tide-wave at those hours, 



140. Describe the cotidal lines. Why is the tide-wave convex 
forward in channels ? How can there be four tides in a day at any- 
place ? 



EFFECT OF COASTS. 117 

respectively. And in the channel which extends 
northward, the wave, having separated from the ocean 
tide, advances northward, and occupies the places 
marked at the hours indicated. The wave advances 
most rapidly in the deepest water. Hence, the front 
is generally convex, as in Eig. 29, since it moves fast- 
est in the central part, where the water is deepest. 
For this reason, also, the tide may occupy as long a 
time in running through a long channel of shallow 
water as in advancing half round the earth. The 
greatest velocity of tide in the deep open ocean is 
near 1,000 miles per hour. Some channels are 
affected by tides entering at both extremities. For 
example, the German Ocean and English Channel 
receive the Atlantic tide both at the north and at 
the south end. As a consequence, the tide system is 
doubled, causing, at some points, four tides per day. 

141. Modification in the Height of the Tide caused 
by Coasts. — The relation of coast lines to each other 
also very much affects the height of the tide at partic- 
ular places. When the tide directly enters a broad- 
mouthed bay, it grows higher as the bay contracts in 
breadth ; and at the head of the bay there is usually 
found the greatest height of all. One of the most 
remarkable examples is the Bay of Eundy. The 
western extremity of the Atlantic tide-wave, after en- 
tering this bay, is gradually contracted by the shores 
as it advances, till, at the head of the bay, it some- 
times rises to 70 feet. 



141. How is the height of the tide affected by the coasts ? Where 
is the tide likely to he highest in a hay ? 



118 LONGITUDE — TIDES. 

The height of the tide on the coast is generally 
greater than in the open ocean, owing to the effect of 
shoal water. The most advanced part of the wave 
moves slower than the hinder portion ; so that the 
cross-section of the ridge becomes shorter, and, there- 
fore, higher, as the depth of water diminishes. 

The mean height of the spring tides at any place 
is called the Unit of Altitude for that place. 

142. Tides of Lalces and Inland Seas. — In general, 
the tides of lakes and inland seas are scarcely per- 
ceptible. The reason is, their extent is so small that 
all parts are to be considered as almost equi-distant 
from the moon. There is little opportunity for water 
to be attracted from the more distant to the nearer 
part. The largest North American lakes have tides 
but an inch or two in height. In the Mediterranean, 
however, which derives no tide from the ocean, the 
tide-wave reaches 1^ or 2 feet. 



142. Why is there so little tide in inland seas ? 



CHAPTER XI. 

THE PLANETS — TABULAR STATEMENTS— MERCURY— 
"VENUS — MARS. 

143, Names and Classification of the Planets.— The 

Planets are solid spherical bodies revolving about the 
sun in orbits which are nearly circular. The name 
"planet" signifies a wanderer, and was given to these 
bodies because they continually change their places 
among the fixed stars, generally moving from west to 
east, but sometimes from east to west. These appar- 
ently irregular motions are fully explained by our 
own annual motion, the earth on which we live being 
one of the planets. 

The planets are naturally arranged in three classes. 

1. Four small planets near the sun, of which the 
earth is the largest, namely : Mercury, Venus, Earth, 
Mars. 

2. The Planetoids, an indefinite number of bodies, 
too small to be measured with certainty, and occupy- 
ing a ring outside of the first class. They are also 
called Asteroids and Minor Planets. 



143. What are planets ? State and describe the three groups. 



120 THE PLANETS. 

3. Four large planets, moving outside of the ring of 
planetoids, widely separated from each other, and at 
vast distances from the sun. These are Jupiter, 

Saturn, Uranus, Neptune, 

Two planets of the first class, Mercury and Yenus, 
revolve in orbits within the earth's orbit. These are 
called inferior planets, being loiver down in the solar 
system than the earth is. All the others, including 
the planetoids, are called superior planets ; because, 
in relation to the sun, the great center of attraction, 
they are higher than the earth, and revolve in orbits 
exterior to the earth's orbit. 

144. Satellites.— There is another class of spheri- 
cal bodies, holding a subordinate place in the solar 
system, since they revolve around the planets as cen- 
ters. These are called Satellites. The moon, already 
described in Chapter VIII, is a satellite of the earth. 
They are distributed as follows : • The earth has 1 ; 
Jupiter, 4 ; Saturn, 8 ; Uranus, 4 ; Neptune, 1. Mer- 
cury, Yenus, and Mars, have no satellites. 

The satellites are also called secondary planets; 
and the planets, in distinction from them, primary 
planets. 

145. Distances of the Planets from the Sun. — The 

following table presents the mean distances of the 
planets from the sun in millions of miles, and also 
their relative distances, the earth's being called 1 : 



144. V\That are satellites j What planets do they attend ? 

145. Give the distances of the planets from the sun. 



PEEIODIC TIMES. 121 

I. Mean Relative 

Distances. Distances. 

Mercury 37,000,000 0.39 

Venus 69,000,000 0.72 

Earth 95,000,000 1.00 

Mars 145,000,000 1.52 

Planetoids 254,000 000 2.67 

Jupiter 496,000,000 5.20 

Saturn . . . . 909,000,000 9.54 

Uranus 1,828,000,000 19.18 

Neptune 2,862,000,000 30.04 

It appears, by this table, that the remotest planet 
is 77 times as far from the sun as the nearest. Hence 
it is that orreries, unless of inconvenient size, always 
fail of truly representing the planetary distances. 
The same is generally true of diagrams. 

146* Periodic Times of the Planets. — The follow- 
ing table contains the length of the sidereal revolu- 
tions in months and years, which is the most con- 
venient form for the memory ; their length in days 
and decimals, for calculations ; and their mean daily 
motion : 

IL 

Sidereal Sidereal Revolu- Mean Daily 

Revolution. tion in Days. Motion. 

Mercury 3 months. 87.969 4° 5' 22.6" 

Venus 7± ■ " 224.701 1° 36' 7.7" 

Earth 1 year. 365.256 0° 59' 8.3" 

Mars 2 "• 686.980 0° 31' 26.5" 

Planetoids 4-|- " 

Jupiter 12 " 4,332.585 0° 4' 59.1" 

Saturn 29 " 10,759.220 0° 2' 0.5" 

Uranus 84 " 30,686.821 0° 0' 42.2" 

Neptune 164 " 60,126.720 0° 0' 21.6" 



146. State the periods of revolution. 



Diameters. 


Volumes. 


82' 2" 


1,405,000 


0' 8" 


* 


0' 17" 


ft 




1 


0' 6" 


t 


0' 37" 


1,521 


0' 16" 


921 


0' 4" 


87 


0' 2" 


79 



122 THE PLANETS. 

147* Magnitudes of the Planets, — Table III gives 
the diameters of trie sun and planets in miles, with 
their mean apparent diameters, and their volumes 
compared with the earth : 

III. 

Diameters. 

Sun 886,000 

Mercury 3,100 

Venus 7,800 

Earth 7,912 

Mars 4,500 

Jupiter 91,000 

Saturn 77,000 

Uranus 35,000 

Neptune 34,000 

148* Masses and Densities of the Planets. — Table 
IV exhibits the masses and densities of the sun and 
planets, the earth being called I. It appears, from 
this table, that the small planets are much more 
dense than the large planets and the sun : 

iv. 

Masses. Density. 

Sun 355,000.00 0.25 

Mercury 0.12 1.97 

Venus 0.88 0.92 

Earth 1.00 1.00 

Mars 0.13 0.72 

Jupiter 338.03 0.22 

Saturn 101.06 0.11 

Uranus 14.79 0.15 

Neptune 24.65 0.31 



147. Give their diameters and volumes. 

148. Also their inasses. Which aie the most dense ? 



PLANETARY MOTIONS. 123 

149. The Sun and Planets Compared. — By Table 
III, we see that the sun has 10 times the diameter, 
and 1,000 times the volume, of Jupiter, the largest 
planet in the system. Table IY shows that the mass 
of the sun is also more than 1,000 times as great as 
that of Jupiter, and 700 times greater than the united 
masses of all the planets. Its attraction mainly con- 
trols the movements of all the planets, satellites, and 
comets. Hence, these bodies describe their various 
paths about it, scarcely disturbing it from a state of 
rest. For this reason, this system of bodies is called 
the Solar System. 

ISO* Diameters of Planets, and their Distances 
from the Sun. — One of the most remarkable facts 
relating to the planets is brought to view in com- 
paring the distances in Table I with the diameters in 
Table III. "While the diameters of the planets are 
only a few thousands of miles, their distances from 
the sun are many millions. The diameter of Nep- 
tune's orbit is more than 20,000 times the diameters 
of all the planets added together. To attempt to 
represent both the distances a*ad magnitudes of the 
planets in their proportions, by an orrery or diagram, 
is out of the question. 

151. Directions of the Planetary Motions, — It has 

been stated in preceding chapters that all the mo- 
tions of the sun, earth and moon are from west to 



149. Compare the sun with the planets in diameter, in volume, 
and in mass. Why is the system called the solar system ? 

150. Compare the diameters of the planets and their distances 
from the sun. 



124 



THE PLANETS. 



east. The same thing is true, in general, of all the 
planets and satellites ; and in nearly every case the 
inclination to the ecliptic is very small. Since the 
motions in the solar system are so generally from 
west to east, this is regarded as direct motion ; and 
any motions, real or apparent, which are from east to 
west, are called retrograde. 

MERCURY. 

152. Apparent 3Iotions. — Mercury is an inferior 
planet, whose orbit is far within the earth's ; for it is 
seen alternately east and west of the sun, and never 



Fig 




more than 29° from it. Let E (Fig. 30), be the earth, 
supposed, for the present, to be at rest ; the circle 



151. What is the general direction of the planetary motions ? 



MEKCUKY. 125 

ABD, the orbit of Mercury ; S, the sun ; and BA/, 
the sky, on which the bodies are seen projected. 
When Mercury is at B, it is seen at B' ; as it passes 
through D to A, it appears to advance to A ; as it is 
now coming toward the earth, it seems to be station- 
ary at A' ; then from A through C to B, it appears to 
retrograde from A to B', where it is again stationary, 
as it moves away from us. Since the sun appears at 
S f , the planet passes by it, both when advancing and 
when retrograding. 

When the planet is at D and C, it is in conjunction 
with the sun ; at C, between the earth and sun, it is 
said to be in the inferior conjunction ; at D, in supe- 
rior conjunction. B and A are called the points of 
greatest elongation. At superior conjunction, the mo- 
tion of Mercury appears to be forward ; at the infe- 
rior conjunction, backward ; and if the earth were at 
rest, as we are now supposing, the planet would ap- 
pear stationary at the points of greatest elongation, 

153. The Motions of Mercury as Modified by the 
Earth's Motion. — To simplify the case, it was sup- 
posed, in the preceding article, that the earth is at 
rest. But the earth moves in nearly the same direc- 
tion as Mercury, making about one revolution while 
Mercury makes four (Table II). The effect is to 
lengthen the arc of apparent advance, and shorten 
that of retrogradation. Thus, let the earth be at A 
(Fig. 31), when Mercury is at F ; then it will appear 
in the sky at L. While the earth is advancing to B, 



152. Describe the apparent motions of Mercury, the earth being 
at rest. Define superior and inferior conjunctions, and greatest 
elongations. 



126 



THE PLANETS. 



Mercury passes the inferior conjunction, and arrives 
at G, and appears at M, having moved apparently 
backward from L to M. As the earth moves to C, 
Mercury describes GKE, and is at superior conjunc- 
tion N. Again, while the earth moves to D, Mercury 



Fig. 31. 




passes round to G, still advancing in the sky to O. 
But while the earth describes DE, Mercury again 
passes the inferior conjunction from G to K, and ap- 
parently retrogrades from O to P; after which, it 
begins once more to advance. Thus, by the earth's 
motion, the planet is made to retrograde through a 
shorter arc, and to advance through a longer one, 
than if the earth were at rest. 



153. Show how the earth's motion modifies the apparent motions 
of Mercury. 



MEECUEY. 127 

154. Stationary Points. — If the earth were at 
rest, as supposed in Fig. 30, the points where the 
planet would appear to be stationary, in relation to 
the stars, would be A and B, at which tangents drawn 
from the earth would meet the orbit. But the earth's 
motion removes the apparently stationary points a 
little way toward the inferior conjunction. For, in 
order to appear stationary, the advance which the 
earth's motion causes must be just neutralized by the 
retrogradation of Mercury. This planet appears sta- 
tionary when its elongation from the sun is 15° or 
20°, according as it is nearer the perihelion or the 
aphelion. 

155. Form and Position of Mercury' s Orbit. — The 

orbit of Mercury is more eccentric, and more inclined 
to the ecliptic than that of any other of the eight 
planets. While the eccentricity of the earth's orbit 
is only ■£$, that of Mercury is nearly ^. Yet this ren- 
ders the minor only -^ shorter than the major axis ; 
so that the form of the most eccentric of the plane- 
tary orbits, if correctly drawn, would appear to the 
eye to be a circle. 

The inclination of Mercury's orbit to the plane of 
the ecliptic is 7°. 

156. Phases of Mercury. — At the inferior con- 
junction, C (Fig. 30), the unilluminated side of Mer- 
cury is turned toward the earth, so that, like the new 
moon, it is invisible. At the superior conjunction, D, 



154. Where would Mercury appear stationary, if the earth were 
at rest ? Where, if the earth is in motion ? 

155. State the form and position of Mercury's orbit. 



128 THE PLANETS. 

its illuminated side is toward us, and it is full. At A 
or B, where the ray AS, and our line of vision, AE, 
are at right angles, the phase is a semicircle. On the 
arc ACB occur the crescent phases ; on BDA, the 
gibbous phases. 

157. Point of Greatest Brightness. — Mercury is 
not brightest when full, because it is then too far dis- 
tant. It is not brightest when nearest, because its 
dark side is toward us. Nor is it brightest at the 
place of greatest elongation ; but beyond it, toward 
the superior conjunction, when about 22° from the 
sun. Its apparent diameter, when nearest the earth, 
and when most distant from it, is as 2J to 1. 

158. Transits of 3Iercury. — As Mercury, at the 
inferior conjunction, passes nearly between the earth 
and sun, it may possibly come exactly in a line with 
them, and thus be seen as a black round spot going 
across the sun's disk. This phenomenon is called a 
transit of Mercury. If the plane of its orbit were 
coincident with that of the ecliptic, a transit would 
obviously occur at every inferior conjunction. Since 
the angle between the two planes is 7°, the planet 
cannot be seen on the disk unless near the node. 
The nodes of Mercury's orbit lie in those parts of the 
heavens which the sun passes through in May and 



156. Describe the phases of Mercury, and when they respectively 
occur. 

157. Where is Mercury when brightest ? Why not at the point 
nearest to us ? 

158. What is a transit of Mercury ? Why does not a transit oc- 
cur at every inferior conjunction ? In what months do they occur ? 



VENUS. 129 

November. Therefore, a transit of that planet can 
occur only in those months. The shortest interval 
between two transits of Mercury is 3J years. 

VENUS. 

159* Apparent Motions. — Like Mercury, Venus 
appears to pass back and forth by the sun, reaching 
a distance of 47° at its greatest elongation. This 
proves it to be an inferior planet, between Mercury 
and the earth. Its sidereal period approaches so 
near to that of the earth that its synodic period is 
lengthened to nearly If years. Hence, after making 
an apparent retrograde motion, as LM (Fig. 31), it 
advances once and two-thirds round the heavens be- 
fore it commences the next retrograde arc, OP. 

160* Phases and Brightness of Venus, — Venus 
passes through the same changes of phase as Mer- 
cury. But its apparent diameter, when the crescent 
phase is narrowest, is more than 6 times as great as 
when at full, because it is more than 6 times as near. 

Venus is the brightest of the planets, and has been 
known from ancient times as the morning and evening 
star, according as it west of the sun, or east of it. 

The place of greatest brightness for Venus is when 
about 40° from the sun, between the point of great- 
est elongation and the inferior conjunction. In this 
situation, it is frequently visible all day. 

161. Transits of Venus. — The orbit of Venus is 
inclined to the ecliptic about 3J degrees. The sun 



159. Describe the apparent motions of Venus. 

160. State respecting its phases and its greatest brightness. 



130 THE PLANETS. 

passes its nodes in June and December. Therefore, 
the transits of that planet always occur in those 
months. 

The shortest interval between two transits of 
Venus is 8 years ; but after the occurrence of two 
such, there cannot be another for more than a cen- 
tury. Between 1800 and 1900 there are two transits 
of Yenus, viz. : December 8th, 1878, and December 
6fch, 1882. 

A transit of Venus is an occurrence of great inter- 
est to astronomers, because it furnishes the best 
method known for determining the sun's horizontal 
parallax, and, therefore, the earth's distance from the 
sun. 

MAES. 

102. Situation of Mars in the Solar System.— This 
is the most remote planet of the first group described 
in Art. 258, namely : Mercury, Venus, Earth, Mars. 
It is also the nearest to the earth of those planets 
which are called superior. 

As Mars revolves in an orbit outside of the earth's, 
it can come into Opposition to the sun, as well as into 
conjunction with it, appearing at every degree of 
elongation from 0° to 180°. 

163. Apparent Motions.— The real motion of Mars 
is from west to east ; and during most of the year, its 
apparent motion is in the same direction, sometimes 



161. What is the shortest interval between two transits of Venus? 
After two such transits, how long before another ? Why is a tran- 
sit of Venus important ? 

162. Where is Mars in the solar system ? What is the opposition 
of Mars ? 



MAES. 



131 



accelerated, and sometimes retarded, by the earth's 
motion. Near opposition, however, when the earth 
overtakes and passes by Mars, its motion appears re- 
trograde. Thus, let the earth make one revolution 



Fm. 32. 




from F to F again (Fig. 32), while Mars describes 
nearly a half revolution from G to N. When the 
earth is at F, Mars appears in the direction FG; 
when at A, Mars, at H, appears in the sky at O ; when 
the earth is at B, Mars, at I, appears at P. Thus far 
the motion has been in advance, though becoming re- 
tarded near P. But as the earth passes from B, 
through C, to D, Mars, passing over the shorter arc 
IKL, appears to retrograde from P to Q ; after which 
it again advances, appearing at B, when the earth is 
at E, and in the direction FN when the earth is at F. 
For the same reason, all the superior planets have 
a retrograde motion at the time of opposition. 



163. By Fig. 32, describe" tlie apparent motions of Mars, When 
will it appear to go backwards ? 



132 



THE PLANET 



164. Phases, and Changes of Apparent Size, — At 
opposition, M (Fig. 33), and at conjunction, M', it is 




obvious that Mars appears full, since we look in the 
same direction in which the sun shines upon it. In 
other positions, the angle between the sun's rays and 
our visual line is acute, and the phase is gibbous (Art. 
101). The planet is so near us that the phase differs 
perceptibly from the full, when about half-way from 
conjunction to opposition, as at Q, Q'. 

The least possible distance of Mars from the earth, 
at opposition, is 35,000,000 miles ; and the greatest 
possible distance, at conjunction, is 255,000,000 miles. 

165. Appearance of Disk. — Mars is remarkable 
among the planets for its redness. The telescope 



164. What changes of phase has Mars? How near the earth, 
and how far from it, can Mars be ? 



MARS. 133 

reveals some permanent inequalities of surface, by 
which its diurnal rotation has been determined more 
satisfactorily than in the cases of Mercury and Ye- 
nus. And there are other appearances, which change 
as the relation of the equator to the sun changes. 
The polar regions, when turned away from the sun, 
exhibit a whiteness which is supposed to be the effect 
of ice and snow ; and this whiteness disappears grad- 
ually when the pole is turned again toward the sun. 

166. Orbit and Equator of Mars. — The orbit of 
Mars is inclined to the ecliptic nearly 2°, and has an 
eccentricity equal to T \. 

In its diurnal rotation, it considerably resembles 
the earth, having about the same length of day, and 
its equator being inclined nearly 29° to its orbit. 
Hence, the seasons vary somewhat more than those 
on the earth. 

The four small planets are all nearly alike as to the 
length of their day. Mercury revolves in 24Ji. 5rn. } 
Yenus in 23h. 21m., the earth in 23k 56m., and Mars 
in 24Ji. 37m. 



165. Describe its telescopic appearance. 

166. What are the form and position of its orbit ? What is the 
length of day on the four planets nearest the sun ? 



CHAPTER XII. 

THE PLANETOIDS — JUPITER— SATURN — URANUS — NEP- 
TUNE — DISTURBANCES OF THE PLANETS. 

107 • Hie Space between the Four Small Planets 
and the Four Large Ones. — There is a wide space 
between Mars and Jupiter, within which the astrono- 
mers of the last century conjectured there might re- 
volve another planet. The search for such a planet 
at length led to the discovery of those bodies called 
the Planetoids, known, also, by the name of Asteroids. 

THE PLANETOIDS. 

108* Their Number, and the Time of their Dis- 
covery. — Four of these bodies were discovered within 
the first seven years of the present century, namely : 
Ceres, Pallas, Juno, and Yesta. Since 1845, others 
have been found nearly every year, till their number 
at the present time (1867) is between 90 and 100. The 
whole number of planetoids may be regarded as in- 
definitely great. 

169. Characteristics.— -They are distinguished from 
the eight planets in the following particulars : 



167. What is said of the space between Mars and Jupiter? What 
was discovered in it ? 

168. Give an account of the discovery. 



THE PLANETOIDS, 135 

1. By their Diminutive Size. — They are invisible to 
the naked eye, and by the telescope cannot be distin- 
guished from faint fixed stars, except by their motion. 
They are generally too small to show a sensible disk, 
and hence cannot be measured with any certainty. 
The largest of them is believed to be only about 200 
miles in diameter. And it is estimated, by the slight 
disturbing influence which they exert, that their entire 
mass is equal only to a small fraction of the earth. 

2. By the Large Eccentricity and Obliquity of their 
Orbits. — The eccentricity of most of them is much 
greater than that of any of the eight planets. 

The obliquity of the orbit of Hebe is 14°, and that 
of Pallas is 34°, which is the greatest yet discovered. 

3. By their being Clustered in a Ring. — The orbits 
vary considerably in size, and, therefore, the periodic 
times are various. But as they are generally quite 
eccentric, every planetoid is nearer the sun at perihe- 
lion than any other one is at aphelion. The orbits are, 
therefore, all linked together, and pass through each 
other. Thus, the planetoids are to be regarded as 
moving among each other about the sun, within the 
limits of a ring, whose breadth, in the direction of 
the radius vector, is more than 100,000,000 miles. 
Flora, which moves in the smallest orbit yet discov- 
ered, performs its revolution in 3 J years ; Cybele, the 
most remote, in 6J years. Their mean periodic time 
is 4J years ; and their mean distance from the sun is 
254,000,000 miles. 



169. What is the first particular which distinguishes the planet- 
oids from the planets? the second? the third? What are the 
longest and shortest periods of the planetoids ? 



136 THE PLANETS. 

JUPITER. 

17 Oo Jupiter's Magnitude and Place in the Solar 

System. — Jupiter is the nearest of the large planets 
outside of the planetoids, and its orbit is not far from 
200,000,000 miles beyond the ring which includes 
them. On account of its great distance from the sun, 
compared with the earth's, Jupiter presents to us no 
visible change of phase, appearing always full. Its 
disk, as presented to us, is almost the same as if we 
were at the sun. The same is, of course, true of all 
the planets still more remote. 

Jupiter greatly surpasses all the other planets in 
magnitude. In volume, it is about 1| times the sum 
of all the others, and in mass, more than 2-J times 
their united mass. 

171. Its Form and Orbit. — Though the diameter 
of Jupiter is 11 times that of the earth, yet it rotates 
on its axis in less than 10 hours ; so that the equa- 
torial velocity is about 27 times as great as the 
earth's. This rapidity of rotation produces a sensi- 
ble oblateness of the planet. Its ellipticity is T \ ; 
and so considerable a deviation from the spherical 
form is perceptible to the eye without measurement. 

The orbit of Jupiter is nearly in the plane of the 
ecliptic, and has an eccentricity of J-q, which is three 
times that of the earth's orbit. The equator of the 



170. Where is Jupiter in the solar system? Does it present 
changes of phase ? Why ? Compare its size and mass with those 
of the other planets. 

1 71 , How swiftly does it rotate on its axis ? What is the effect ? 
Is there a change of seasons on Jupiter ? Why ? 



JUPITER. 



137 



planet is inclined only about 3° to the plane of its 
orbit, so that there is no perceptible change of 
seasons. 

172. The Belts of Jtipiter. — This name is given to 
bands or stripes of darker shade than the rest of the 
disk, stretching across it in the direction of its rota- 

Fig. 34. 




tion (Fig. 34). xhey vary, from time to time, in num- 
ber and in breadth, often covering a large part of the 
surface. A belt usually appears of uniform breadth 
entirely across, but not always ; its edge is occasion- 
ally broken, and sometimes it is much wider on one 
part of the disk than on the other, the change of 
breadth being commonly quite abrupt, and thereby 
revealing the rotation of the planet. There are, ordi- 
narily, two conspicuous belts, lying near the equator, 
one north, and the other south of it. 

Jupiter is supposed to have an atmosphere, in 
which there are always many clouds floating. These, 



172. Describe tlio belts. Explain their formation. 



138 THE PLANETS. 

by the swift rotation of the planet, are thrown into 
stripes parallel with the equator ; and the dark belts 
are considered to be the spaces between the clouds, 
through which we look upon the planet itself. 

173. Satellites of Jupiter. — These are four in num- 
ber, revolving in orbits very nearly circular, and in 
planes which make small angles, both with the orbit 
and the ecliptic. They are called the first, second, 
third, and fourth, reckoning outward from the planet. 
Their orbits being presented edgewise to us, they 
seem to move back and forth across the place of Ju- 
piter, one way in front of the planet, and the other 
w^ay behind it, and always appear nearly in a straight 
line. (See Tig. 34.) 

Jupiter's satellites are all somewhat larger than the 
moon, but on account of their great distance from us, 
they are too small to be seen except by a telescope. 
Because of the great attraction of Jupiter, exerted 
upon them, they revolve a great deal quicker than 
the moon about the earth, as shown in the following 
table : 

Satellites. Diameters. Distances. Sidereal Revolutions. 

1 2,440 275,000 Id. lSd. 28m 

2 2,190 438,000 M. ISh. 15m 

8 3,580 698,000 7d. Sh. 43m. 

4 3,060 1,229,000 16d. 16A. 32m. 

. 174:. Eclipses of Jupiter and its Satellites, — On 

account of the great size of Jupiter and its shadow, 



173. How many satellites lias Jupiter ? How do they appear to 
move ? Give their sises and times of revolution. Why do they re- 
volve so swiftlv ? 



JUPITEK. 139 

and the small inclination between its own orbit and 
those of its satellites, most of them are eclipsed at 
every revolution, when on the opposite side of the 
planet from the sun ; and they generally eclipse Jupi- 
ter itself in passing between it and the sun. And 
since they revolve very rapidly, these eclipses are oc- 
curring every day. When Jupiter is eclipsed by one 
of its moons, there is seen only a small dark spot 
going across its disk. Both kinds of eclipses will be 

Fig. 35. 





understood by reference to Fig. 35, where J repre- 
sents Jupiter, 1, 2, 3, 4, the orbits of the satellites, 
and A, B, C, D, different positions of the earth in its 
own orbit. At a, the first satellite is just entering the 
shadow ; at b, it has just emerged ; and when any 
satellite comes between J and the sun, its shadow will 
fall on the planet. 

By means of the eclipses of Jupiter's satellites it 
has been discovered how swiftly light moves. For, 
when the earth is at A, it is observed that an eclipse 



174. What phenomena do they present ? Describe and explain 
the eclipses of the satellites and of the planet. What discovery 
was made by these means ? 



140 



THE PLANETS. 



is seen about 16 minutes earlier than if it were at C. 
And this must be because it requires 16 minutes for 
the light to cross the earth's orbit. 

SATURN. 

.175, Saturn's Disk. — Saturn is the second planet 
in size ; and being the second in order beyond the 
planetoids, is not too far from the earth to present a 
large disk. Its form is seen to be elliptical, and it is 
faintly striped with belts in the direction of the major 
axis. Both these appearances are explained by the 
rapid rotation of the planet on its axis, as in the case 
of Jupiter. It 
ellipticity is ^ 



revolves in about 10J hours, and its 



176, Saturn's Mings. — The distinguishing feature 
of this planet is the system of broad thin rings which 

Fig. 36 




surround it. They lie in a plane inclined about 28° 
to the ecliptic, and, therefore, generally present an 



175. Where is Saturn's place in respect to distance from the sun ? 
In respect to size ? What is the appearance of its disk ? 



SATURN. 



141 



elliptical appearance to the earth (Fig. 36). The 
ring, as usually seen, consists of two rings, the inner 
of which is the widest. The inner edge is 20,000 
miles from the surface of the planet ; and the diame- 
ter from outside to outside is 176,000 miles. The line 
in which the plane of the ring intersects the plane of 
Saturn's orbit is called the line of the nodes. 

The rings revolve in the same time as the planet ; 
that is, in about 10 J hours. 

177. Disappearance of the Mings. — Saturn re- 
volves about the sun once in 29 years, and its rings 
always remain parallel to themselves, as represented 

Fig. 37. 




in 'Fig. 37, where GO is Saturn's orbit, and db the 
earth's. As Saturn moves from A, through C, to E, 
we look upon the northern side of the rings ; and 



176. What distinguishes Saturn? Describe the rings and their 
motions. 

177. What is Saturn's period ? What are the changes in the as- 
pect of the rings ? Can the rings disappear more than once during 
the year of disappearance ? Why ? 



142 THE PLANETS. 

from E to A, upon the southern side. At A and E, 
the rings present their edge toward us, and can 
scarcely be seen at all. Thus, the rings disappear 
once in about 15 years. 

But it requires about a year for the plane of the 
rings to pass by the whole breadth of the earth's 
orbit. It, therefore, happens that, during the year of 
the edge-view, the plane will pass once through the 
sun, and perhaps two or three times through the 
earth ; and, during a portion of the year, the plane 
will He between the sun and the earth, so that the 
dark side of the rings will be presented toward us. 

1 78, Phenomena of the Mings at the Planet. — On 

that hemisphere of the planet to which the luminous 
side of the rings is presented, there is the appearance 
of splendid arches spanning the sky, having a breadth 
and elevation according to the latitude of the place. 
At latitude 30° the breadth is about 18°, and the ele- 
vation of the lower edge on the meridian about 22°. 
Near the poles, however, it is below the horizon. The 
luminous side is presented to the northern hemisphere 
near 15 years, and then the same length of time to the 
southern hemisphere, in regular alternation. 

A part of the rings is generally eclipsed by the 
shadow of the planet falling on it. 

Also, during the 15 years in which the dark side of 
the rings is turned toward a hemisphere, its shadow 
is cast across a zone of it, which causes an eclipse of 
the sun. And at a given place, a total solar eclipse 
may continue from day to day, without interruption, 
for several years. 

178. How do tlie rings appear on the planet itself? 



UEANUS. 143 

179, Satellites of Saturn, — Saturn is attended by 
eight satellites. Their periods of revolution vary 
from less than one day to 79 days. Their diameters 
vary from 500 to 3,000 miles ; but on account of their 
immense distance from the earth, they are seen only 
with the best instruments. They are all external to 
the rings, at distances from the planet varying from 
129,000 to 2,478,000 miles. Their orbits are nearly 
in the plane of the rings, and make an angle of about 
28° with the orbit of the planet. Hence, they are 
not very liable to be eclipsed. The principal time for 
eclipses is that at which the rings disappear ; for 
then the sun is nearly in the plane of their orbits, as 
well as of the rings. 

URANUS. 

180* Discovery, and Place in the System. — Uranus 
was unknown to the ancient astronomers ; and to 
them, therefore, Saturn's orbit was the boundary of 
the solar system. Uranus was discovered by Sir 
William Herschel, in 1781, and has made but little 
more than one revolution since that time ; for its 
periodic time is 84 years. It was, however, repeat- 
edly seen by earlier astronomers, and recorded in 
their catalogues as a fixed star. By this discovery, 
the diameter of the known solar system was doubled. 

Uranus is the third of the four great planets, both 
in size and in order of distance. But its distance 
from us is so immense that it appears only as a faint 



179. Describe the satellites of Saturn. 

180. When, and by whom, was Uranus discovered ? How dees 
it appear ? 



144 THE PLANETS. 

star, and presents no inequalities by widen its diurnal 
motion can be discovered. Its orbit is very nearly 
circular, and is inclined less than a degree to the 
ecliptic. 

181. The Satellites of Uranus. — Sir William Her- 
schel announced the discovery of six satellites belong- 
ing to Uranus. But only four have been identified 
by later astronomers. The remarkable facts relating 
to these satellites are, that their orbits are nearly at 
right angles to the plane of the ecliptic, and that in 
the orbits the motions of the satellites are retrograde; 
that is, from east to west. Their periods of revolu- 
tion vary from 2J days to 13J days, and their dis- 
tances from 130,000 to 396,000 miles. 

NEPTUNE. 

182. Discovery. — Neptune was discovered in 1846. 
The circumstances which led to the discovery were 
briefly as follows : After the orbit of Uranus had 
been carefully computed, and corrections made for 
the disturbing influence of Jupiter and Saturn, the 
planet was found to depart from the calculated path 
in a manner not to be accounted for except by sup- 
posing some other disturbing force. It was for some 
time suspected that there must be a planet superior 
to Uranus, whose attraction caused the change of its 
orbit. At length, two mathematicians, Le Verrier, of 
France, and Adams, of England, each without any 
knowledge of what the other was attempting, engaged 



181. By what is it attended ? 



NEPTUNE. 145 

in the arduous labor of calculating what must be the 
elements of a planet which should produce the given 
disturbance of the motions of Uranus. They reached 
results which agreed remarkably with each other D 
Le Verrier communicated to Galle, of the Berlin ob- 
servatory, the place in the sky in which the disturb- 
ing body should be situated ; and in the evening of 
the same day, Galle found it within a degree of the 
predicted longitude. 

The planet thus discovered explains fully the dis- 
turbances in the motions of Uranus. 

It soon appeared that Neptune had repeatedly 
been entered in catalogues as a fixed star. The ear- 
liest of these records, in 1795, afforded material aid 
at once in determining its mean distance and its peri- 
odic time. 

Neptune is attended by one satellite, which was 
also discovered in 1846. It is nearly as far from the 
primary as the moon is from the earth, and revolves 
in 5d. 21h. 

So far as known, Neptune is the most remote- 
planet of the solar system, its distance from the sur 
being 30 times as great as that of the earth. Its 
time of revolution is 164 years. 

MUTUAL ACTION OF THE PLANETS. 

183. Motions of the Planets Disturbed. — On ac- 
count of the universal gravitation of matter, it mighl 
be expected that the planets, in describing theii 



182. When was Neptune discovered? What led to the discov 
ry? Give an account of it. State other particulars respecting 
Neptune. 



146 THE PLANETS. 

orbits about the sun, would disturb each other's mo- 
tions. It is true that they do ; and one of the most 
difficult and laborious parts of practical astronomy is 
to calculate and allow for these disturbances. No 
one of all the planets pursues the same elliptic orbit 
which it would describe if the sun were the only other 
body in the system. 

One kind of disturbance is this : The plane of an 
orbit changes its position in such a manner that the 
nodes, in which the planet cuts the plane of the 
ecliptic, move backward ; that is, from east to west. 
Another is, that the perihelion and aphelion of most 
planetary orbits advance, or move from west to east. 
Still another disturbance is, that the eccentricity of an 
orbit changes, becoming at one time greater, and at 
another time less. And others beside these might be 
named. 

184. Stability of the System, — Notwithstanding 
these disturbances, it has been proved that they do 
not tend to cause the destruction of the system, as 
was once supposed. The reasons why the stability 
and permanency of the system are not endangered 
are the following : 

1. The planets are exceedingly small compared 
with the central body, the sun being more than 700 
times greater than all of them together. 

2. The largest planets are very distant from the 



183. What effect do the planets produce on each other? State 
the different kinds of disturbance caused by them. 

184. Do they tend to destroy the system ? Why ? The first rea- 
son — the second. 



STABILITY OF THE SYSTEM. 147 

small ones and from each other, and move in orbits 
very nearly circular, and very nearly in one plane. 

For these ' reasons the disturbances are all very 
small ; and such of them as might ultimately become 
dangerous by accumulating for a long time, are pre- 
vented from accumulating by oscillating back and 
forth ; that is, they increase for a time in one direc- 
tion, and then in the opposite. 



CHAPTEK XIII. 

COMETS — SHOOTING STARS. 

185. A Comet Defined. — A comet is a body which 
consists of nebulous matter, and revolves about the 
sun in a very eccentric orbit. Most comets present a 
roundish ill-defined appearance, often having a bright 
central part, called the Nucleus. The fainter part, 
surrounding the nucleus, is called the Coma (hair) ; 
and the Tail, which distinguishes many comets, is 
merely the extension of the coma. It is the stream- 
ing appearance of the tail, resembling hair, which 
gave the name " comet" to this class of bodies. The 
nucleus has been sometimes supposed to be solid ; 
but it probably consists always of nebulous matter in 
a more condensed state than the other parts. The 
nucleus and coma are called the Bead of the comet. 

186. Number of Comets. — Many hundreds of com- 
ets have been recorded, most of them, of course, vis- 
ible to the naked eye. But lately it is observed that 
most comets are telescopic objects. And many, which 
would otherwise be seen, escape observation by being 
above the horizon only in the daytime. The whole 
number, therefore, belonging to the solar system is 



185. Define a comet and its parts. 

186. What is said of the number of comets 



TAILS OF COMETS 



149 



undoubtedly to be reckoned by thousands, or tens of 
thousands. 

187. Eccentricity of Orbit. — All known cometary 
orbits are more eccentric than any planetary orbit ; 
and most of them are exceedingly so, their perihelion 
being as near the sun as Mercury and Yenus, or 
nearer, and their aphelion as far off as the most dis- 
tant planets, or even beyond. And some appear to 
be ellipses of infinite length. 

On account of this great eccentricity, comets are 
not seen except when they are near the perihelion. 

188. Form and Direction of Tails of Comets.— -The 
forms of tails belonging to different comets are ex- 
ceedingly varied. In general, however, the sides 
diverge from the head, so that the most distant and 
faintest part is broadest, as in the comets of 1680 and 

Fig. 38. 




COMET OF 1680. 



187. What is the form of their orbits? When are the comets 
invisible ? 

188. Describe the general appearance and direction of the tail. 




COMET OF 1811. 

1811 (Figs. 38, 39). But sometimes the divergence is 
very slight, as in the comet of 1843 (see Fig. 40). In 
a few instances, the tail has appeared to be divided 
into two or more branches diverging from each other. 
The general direction of the tail is from the sun; so 
that, as a comet approaches the sun, the tail follows 
it; but as it recedes, the tail is directed forward. 
The axis of the tail is not, however, a straight line, 
but more or less curved backward, so that the convex 
side of the curve is foremost in the motion. 

189. Dimensions of Comets. — The dimensions of 
comets are various, and, on account of their nebulous 
character, they never admit of accurate measurement. 
The nucleus of a large comet is sometimes 5.000 
miles, and the coma 200,000 miles, in diameter, while 
the tail has, in one case, attained the extraordinary 
length of 200,000,000 miles. 



189. What is said of tlie dimensions of comets ? Over how long 
an arc does the tail sometimes extend ? 



MATTER IN COMETS. 151 

The apparent length of a comet's tail is often suf- 
ficient to span an arc of 20° or 30° on the sky, and 
sometimes much more than this. The comet of 1680 
extended 97°, and that of 1861, 106°. The fainter 
part, in all cases, is seen only by indirect vision. 

It is obvious that the real length cannot be inferred 
from the apparent, until the distance from us, and the 
obliquity to our line of vision, are obtained. 

190. Light of the Comets. — These bodies, like the 
planets and satellites, shine by solar light which they 
reflect to us. But, unlike all planetary bodies, they 
are in a condition so attenuated that the sun's rays 
penetrate every part of them without obstruction. 
The brightness of a star is not diminished in the least 
when seen through the tail or coma of a comet. In 
a few instances, a star has been seen through the nu- 
cleus, and even then was not essentially dimmed. 

191. Quantity of Matter in Comets.— Though some 
of the largest comets surpass all other bodies in the 
solar system in magnitude, yet in respect to their mass 
they are too small to have produced, as yet, the 
slightest perceptible effect. They sometimes come 
very near planets and their satellites, but are never 
known to exert the least influence on them. They 
do, of course, attract the planets, because they are 
attracted by them, and suffer great disturbances from 
them. But until they themselves produce some effect 
which is appreciable, their mass must be regarded as 
infinitely small. 

190. What is said of tlie light of the comets ? 

191. What proof is given that their mass is very small ? Do we 
ka / that they attract at all? 



152 COMETS. 

192, Directions of Cometary 3Iotions. — The com- 
etary orbits are unlike the planetary, not only in the 
degree of their eccentricity, but in the varied posi- 
tions of their planes. Instead of being limited to a 
narrow zone like the zodiac, they make every variety 
of angle with the ecliptic, so that a comet is as likely 
to pass round the sun from north to south as from 
west to east. And whether the orbit is much or little 
inclined, the comet's motion in it is as often retro- 
grade as direct. 

193* T7ie Determination of a Comet's Orbit,— From. 
the observations of right ascension and declination of 
a comet, which are repeatedly made while it is in 
sight near the perihelion, the form of its orbit and 
the time of describing it can be calculated. But the 
part in which it is visible is so small, compared with 
the whole orbit, that the results of calculation are 
quite uncertain, until the comet is identified on its re- 
turn. "When a comet is thus identified, its periodic 
time is, of course, known ; and from that the length 
and form of its orbit can be computed. 

The periods of most comets, however, appear to 
be so long that only a few have returned since 
the time when accurate observations began to be 
made. Hence it is that by far the greater part of all 
the recorded comets are unknown in respect to the 
extent of their orbits and the time of describing 
them. And the few which are known have com- 



192. How are their orbits situated ? 

193. What observations are made in order to calculate their or- 
bits ? Are the results certain ? When can the orbits be exactly 
determined ? Have many been determined? 



EEMAKKABLE COMETS. 153 

paratively small orbits, and describe them in short 
periods. 

194. Comets of Known Period. — The following 
table contains the names of the only comets whose 
periodic times are certainly known : 

Period Perihelion Aphelion 

Comet. in years. Distance. Distance. 

Halley's 75 56,000,000 3,400,000,000 

Encke's 3£ 32,000,000 390,000,000 

Biela's 6-J 85,000,000 570,000,000 

Faye's 7i 161,000,000 565,000,000 

Brorsen's 5^ 62,000,000 538,000,000 

D' Arrest's 6i 111,000,000 546,000,000 

Winnecke's 5£ 73,000,000 526,000,000 

Of the above, Halley's is by far the most interest- 
ing, on account of its brightness and length of tail, 
and also on account of its long period. Its last re- 
turn to the perihelion was in 1835, and it will not be 
seen again till 1910. The other six contained in the 
table considerably resemble each other. Their pe- 
riods are short, they are accompanied by little or no 
tail, and they are all too faint to be seen except by 
a telescope. Hence, they are of little interest except 
to the astronomer. 

195. Other Remarkable Comets. — The comet of 
1680 was unusually brilliant, and was the first whose 
orbit was calculated by Sir Isaac Newton. (See 
Fig. 38.) 

The comet of 1744 was so bright as to be seen in 



194. Name the comets whose orbits are known. Which is the 
most interesting ? Why ? What is said of the others ? 



154 COMETS. 

the daytime. Its tail was divided into six distinct 
and divergent parts. 

The comet of 1770 was remarkable for having its 
orbit twice changed by the attraction of Jupiter ; first 
from a period of 48 years to one of 6 years, and then 
again to one of 20 years. While its period was six 
years, it came twice to the perihelion, but was never 
seen before, and has never been seen since. 

The comet of 1843 was so bright as to be seen by 
day, and passed so near the sun at perihelion as to 

Fig. 40 




touch it. Its tail was very slender and straight, as 
shown in Fig. 40. 

The comet of 1858, called, also, Donati's comet, 
presented a series of envelopes, one within another. 
Its period is computed to be about 2,000 years. 

The comet of 1861 was remarkable for the great 
apparent length of its tail, viz., 106°. It came so 



195. Describe tlie comet of 1680— of 1744— of 1770— of 1843— of 

1858— of 1861. 



GASEOUS 



ETEORS. 



155 



near the earth that the latter 
is supposed to have passed 
through a part of its tail. Its 
appearance is presented in 



Fig. 41. 



Fig. 41. 



196. Shooting Stars.— This 
is the popular name given to 
those bodies which appear 
like stars or planets moving 
across some part of the sky, 
and then vanishing. They 
are equally well known by 
the name of meteors. They 
may be seen in any clear 
night, by watching an hour 
or two, especially if the moon 
is not shining. The heights 
of meteors are found to be 
generally about 50 miles, and 
their velocities 20 or 30 miles 
per second. Coming into the 
air with such great velocity, 
they are almost instantly set 
on fire, and their substance 
becomes incorporated with 
the atmosphere. From the 
meteors, it is found that they 
around the sun. 



Jill! 1 



Iftllillljll: 

I 



m 



i;?%-..;. 



m 



:'■*. 



iBl'ili 



11111 jiiii 



observed motions of 
are bodies revolving 



197. Gaseous Meteors. — If the ordinary meteors 



196. What are shooting stars ? How high are they generally ? 
What is their velocity ? Around what do they revolve ? 



156 SHOOTING STARS. 

were more dense than a gas, they would hardly lose 
all their motion, as they do, before reaching the earth. 
The most interesting fact relating to this class of 
bodies is, that they sometimes come in showers; that 
is, hundreds of thousands of them are seen in a 
single night. These showers seem to have periodical 
returns. The most remarkable date is November 
12th or 13th, at which time, every 33 or 34 years, they 
appear in immense numbers on some part or other of 
the earth's surface. 1799, 1833, and 1866 were the 
three last times of great meteoric showers. 

198. Solid Meteors. — There is another class of 
meteoric bodies which afford indubitable evidence of 
being solid. Like the gaseous meteors, they plunge 
into the atmosphere with great velocity, and are in- 
flamed by the violent friction. Before reaching the 
earth they usually explode, and scatter their frag- 
ments. Some of them, however, appear to lose only 
small portions of their mass by explosion, and pass 
on in their orbits round the sun, greatly disturbed, of 
course, by the earth's attraction. 

199. Aerolites. — This is the name usually given to 
the fragments thrown down by solid meteors ; though, 
in rare instances, an aerolite obviously constitutes 
the entire meteor itself. Aerolites consist of iron, 
silex, and a few other materials, which are all known 
among terrestrial substances. But they are always 
distinguishable from terrestrial bodies by their pecu- 



197. Describe meteoric showers. What are the dates of their 
occurrence ? 

198. How is it known that any meteors are solid ? 



AEEOLITES. 157 

liar structure. Since the great velocities of meteors, 
solid as well as gaseous, have become known, the 
former theories as to the origin of meteoric stones, 
or aerolites, have been abandoned. Such velocities, 
if they could be generated at all on the earth, could 
never exist in horizontal or downward directions. 
Both solid and gaseous meteors are, therefore, con- 
sidered as describing orbits about the sun. The inter- 
planetary spaces, which have been generally reckoned 
as vacant, may perhaps be to a great extent occupied 
by innumerable bodies, of a grade far below that of 
comets and planetoids. 



199. What are aerolites ? Of what do they consist ? How is 
their material distinguishable from terrestrial substances ? 



CHAPTEB XIV. 

THE EJXED STAES— CONSTELLATIONS. 

200. The Stellar Universe. — The bodies described 
in the foregoing chapters all belong to the solar sys- 
tem. If our investigations are extended outside of 
this system, we find that there are other systems, 
greater or less than this, unlimited in number, and 
separated from the solar system and from each other 
by solitudes so vast that each system is only a point 
in comparison with the distances between them. The 
central sun in each of these countless systems is a 
fixed star. 

The word "universe" is employed to express the 
sum total of all these systems, the number of which, 
and the extent of space occupied by them, are utterly 
beyond the reach of human comprehension. 

201* The Fixed Stars, and their Magnitudes. — The 
fixed stars are so called because, to common observa- 
tion, they always maintain the same situations with 
respect to each other. All the thousands of bright 
points ordinarily seen in the sky by night are fixed 
stars, with the exception of two or three, possibly 
four, which are planets. 



SCO. What is there outside of the solar system? What is the 
meaning of universe ? 



UNEQUAL BEIGHTNESS. 159 

The fixed stars are classified according to magni- 
tudes, though the word, when thus used, signifies only 
degrees of brightness. The stars which can be seen by 
the naked eye, in the most favorable circumstances, 
are divided into six magnitudes. Those which can 
be seen only by the aid of the telescope, called tele- 
scopic stars, are arranged into several more ; so that 
all the magnitudes are 16 or 18. 

Stars of the same magnitude are not equally bright ; 
for there is a continual gradation in respect to bright- 
ness ; so that, if the intensity were accurately meas- 
ured, probably the light of but very few would be 
found exactly equal. 

Stars of the first magnitude are fewest in number, 
and, generally, the smaller the magnitude, the larger 
the number of stars included under it. The limits of 
the successive magnitudes differ somewhat, according 
to different astronomers ; but the following round 
numbers do not vary widely from any of them : 



First magnitude 20 

Second magnitude 40 

Third magnitude 140 



Fourth magnitude 300 

Fifth magnitude 950 

Sixth magnitude 4,450 



In all, near 6,000, visible to the naked eye. The 
numbers of the telescopic stars increase at so rapid a 
rate that they have to be reckoned by millions. 

202. Cause of Unequal Brightness. — "We might 
suppose either that the stars are themselves unequal 
in respect to the quantity of light which they emit, or 



201. Why are the fixed stars so called ? How are they classified? 
What are telescopic stars ? Give the numbers included under each 
of the first six magnitudes. 



160 CONSTELLATIONS. 

tliat they appear unequally bright on account of their 
different distances. It is undoubtedly true that there 
is some diversity in the bodies themselves ; and yet, 
the rapid increase of numbers as the magnitudes are 
less, indicates that difference of distance is the chief 
cause of inequality in brightness. If there is any 
approach to a uniform distribution of the stars in 
space, those which are nearest should be fewest in 
number, and should, in general, appear brightest. 

203. Constellations. — The fixed stars are also 
classed topographically in constellations. This divi- 
sion is very ancient ; and some of the constellations 
are mentioned by the earliest writers. The names 
given to them are those of the animals, heroes, and 
other objects of pagan mythology. 

"Within each constellation, the brightest stars are 
designated by the letters of the Greek alphabet in 
the order of brightness. Thus, Alpha Lyrse is the 
brightest star in Lyra ; Beta Scorpionis, the brightest 
but one in Scorpio, &c. After the Greek letters are 
all used, Roman letters, and then numerals, are em- 
ployed. In some cases the order of brightness does 
not accord with the order of the alphabet. This may 
result from a change of brightness which has taken 
place since the stars were first named. When a cap- 
ital letter follows a number, there is reference to the 
catalogue of some astronomer. Thus, 84H is the star 
84, of a certain constellation in Herschel's catalogue. 

A few conspicuous stars are still known by the indi- 



202. What is the principal cause of unequal brightness in stars ? 

203. What are constellations ? How are stars in each designated ? 



THE ZODIAC. 161 

vidual names given to them in ancient times ; as Arc- 
turus, Antares, Sirius, Yega, &c. 

204, Star Catalogues. — The first catalogue of stars 
was made by Hipparchus, before the time of Christ, 
and contained 1,022 of the most conspicuous stars. 
Catalogues of the present day contain hundreds of 
thousands of stars, whose right ascensions and de- 
clinations are given for a certain date. 

203. Descriptions of Constellations. — The remain- 
der of this chapter is devoted to brief descriptions of 
the most prominent constellations which can be seen 
in about latitude 40° N., accompanied by a few dia- 
grams to show the relative position of some of the 
principal stars contained in them. These are in- 
tended to afford the learner some aid in studying the 
constellations in the sky. But in order to become 
well acquainted with this branch of astronomy, a 
celestial globe or a series of star maps is necessary. 

CONSTELLATIONS OF THE ZODIAC. 

206. Aries (The Main) the first Aeies. 

constellation of the Zodiac, is known &. 
by two bright stars, Alpha, on the a fi% 

northeast, and Beta, on the southwest, 
4° apart, forming the head. . South of 7 

Beta, at the distance of 2°, is a smaller star, Gamma. 



204. Who made the first catalogue of stars ? Compare the num- 
ber in that and modern catalogues. 

205. What is the purpose of the following descriptions ? What 
more is needed, in order to learn the constellations thoroughly ? 

206. Describe Aries. 



162 CONSTELLATIONS. 

The next brightest star of the Kam, Delta, is in the 
tail, 15° southeast of Alpha. The feet of the figure 
rest on the head of the Whale. 

t 207. Taurus (The Bull) will be readily found by 
the seven stars, or Pleiades, which lie in the neck, 24° 
eastward of Alpha Arietis. The largest star in Tau- 
rus is Aldebaran, of the first magnitude, in the Bull's 
eye, 10° southeast of the Pleiades. It has a reddish 
color, and resembles the planet Mars. The other eye 

Taurus. Pleiades. 

6% 



of the figure is Epsilon, 3° northwest of Aldebaran. 
Five small stars, situated a little west of Aldeba- 
ran, in the face of the Bull, constitute the Hyades. 
Although the Pleiades are usually denominated the 
seven stars, yet it has been remarked, from a high an : 
tiquity, that only six are present. 

Some persons, however, of remarkable powers of 
vision, are still able to recognize seven, and even a 
greater number. With a moderate telescope, not less 
than 50 or 60 stars, of considerable brightness, may 
be counted in this group, and a much larger number 
of very small stars are revealed to the more pow- 
erful telescopes. The beautiful allusion, in the Book 
of Job, to the " sweet influences of the Pleiades," and 



207. Describe Taurus. 



THE ZODIAC. 163 

the special mention made of this group by Homer 
and Hesiod, show how early it had attracted the 
attention of mankind. The liorns of the Bull are two 
stars, Beta and Zeta, situated 25° east of the Pleiades, 
being 8° apart. The northern horn, Beta, also forms 
one of the feet of Auriga, the Charioteer. 

208. Gemini (The Twins) is re- The Twins. 
presented by two well-known stars, „ " 
Castor and Pollux, in the head of * 
the figure, 5° asunder. Castor, the 
northern, is of the first, and Pollux 
of the second magnitude. Four 
conspicuous stars, extending in a 
line from south to north, 25° south- 
west of Castor, form the feet, and 
two others, parallel to these, at the 
distance of 6° or 7° northeastward, 
are in the knees. 



7# 



209. Cancer (The Crab). — There are no large stars 
in this constellation, and it is regarded as less re- 
markable than any other in the Zodiac. The two 
most conspicuous stars, Alpha and Beta, are in the 
southern claws of the figure ; and in its body are the 
northern and southern Asellus, which may be readily 
found on a celestial globe. But the most remark- 
able object in this constellation is a misty group 
of very small stars, so close together, when seen by 
the naked eye, as to resemble a comet, but easily sep- 
arated by the telescope into a beautiful collection of 
brilliant points. It is called Prossepe, or the Beehive. 



208—209. Describe Gemini— Cancer. 



164: CONSTELLATIONS. 

210. Leo (The Lion) is a very large constellation, 
and has many interesting members. Regulus (Alpha 
Leonis) is a star of the first magnitude, which lies 

The L*ion. 

j 

very near the ecliptic, and is much used in astronom- 
ical observations. North of Regulus lies a semicircle 
of five bright stars, arranged in the form of a sickle, 
of which Regulus is the handle, and extending over 
the shoulder and neck of the Lion. Denebola, a con- 
spicuous star in the Lion's tail, lies 25° east of Regu- 
lus. Twenty bright stars in all help to compose this 
beautiful constellation. It ranges from west to east 
along the Zodiac, over more than 40° of longitude, 
all parts of the figure excepting the feet lying north 
of the ecliptic. 

211, Virgo (Hie Virgin) extends along the Zodiac 
eastward from the Lion, covering an equally wide re- 
gion of the heavens, although less distinguished by 
brilliant stars. Spica, however, is a star of the first 
magnitude, and lies a little east of the vernal equi- 
nox. Vindemiatrix, in the arm of Virgo, 18° east of 
Denebola, and 23° north of Spica, is easily found ; 
and directly south of Denebola 13°, is Beta Virgims; 



210—211. Describe Leo— Virgo. 



THE ZODIAC. 165 

while four other conspicuous stars, in the form of a 
trapezium, between this and Vindemiatrix, lie in the 
wing and shoulders of the figure. The feet are near 
the Balance. 

212* Libra (TJie Balance) is composed of a few 
scattered members situated between the feet of Yirgo 
and the head of Scorpio, but has no very distinctive 
marks. Two stars of the second magnitude, Alpha, 
on the south, and Beta, 8° northeast of Alpha, to- 
gether with a few smaller stars, form the scales. 

213, Scorpio (TJie Scorpion) is one of the finest 
of the constellations of the Zodiac, and is manifestly 
so called from its resemblance to the animal whose 



The Scorpion. 



* 
* * 



*v 



* « 



# 



name it bears. The head is composed of five stars, 
arranged in a line slightly curved, which is crossed in 



212—213. Describe Libra— Scorpio. 



166 CONSTELLATIONS. 

the center by the ecliptic, nearly at right angles, a 
degree south of the brightest of the group, Beta Seor- 
pionis. Nine degrees southeast of this is a remarka- 
ble star of the first magnitude, called Antares, and 
sometimes the Heart of the Scorpion. It is of a red 
cjlor, resembling the planet Mars. South and east of 
this, a succession of not less than nine bright stars 
sweep round in a semicircle, terminating in several 
small stars forming the sting of the Scorpion. The 
tail of the figure extends into the Milky Way. 

214. Sagittarius (The Archer). — Ten degrees east- 
ward of the Scorpion's tail, on the eastern margin of 
Milky Way, we come to the hoiv of Sagittarius, con- 
sisting of three stars, about 6° apart, the middle one 
being the brightest, and situated in the bend of the 
bow, while a fourth star, 4° westward of it, consti- 
tutes the arrow. The archer is represented by the 
figure of a Centaur (half horse and half man) ; and 
proceeding about 10° east from the bow, we come to 
a collection of seven or eight stars of the second and 
third magnitudes, which lie in the human or upper 
part of the figure. 

215. Capricornus (The Goat), represented with the 
head of a goat and the tail of a fish, comes next to 
Sagittarius, about 20° eastward of the group that 
form the upper portions of that constellation. Two 
stars of the second magnitude, Alpha, on the north, 
and Beta, on the south, 3° apart, constitute the head 
of Capricornus, while a collection of stars of the 



214 — 215, Describe Sagittarius — Capricornus. 



THE ZODIAC. 167 

third magnitude, lying 20° southeast of these, form 
the tail. 

216. Aquarius (The Water Bearer) is closely in 
contact with the tail of Capricornus, immediately 
north of which, at the distance of 10°, is the western 
shoulder (Beta), and 10° further east is the eastern 
shoulder (Alpha) of Aquarius. About 3° southeast of 
Alpha is Gamma Aquarii, which, together with the 
other two, makes an acute triangle, of which Beta 
forms the vertex. In the eastern arm of Aquarius 
are found four stars, which together make the figure 
T, the open part being westward, or towards the 
shoulders of the constellation. Aquarius ranges 
nearly 30° from north to south, being nearly bisected 
by the ecliptic. 

217. Pisces (TJie Fishes). — Three figures of this 
kind, at a great distance apart, two north and one 
south of the ecliptic, compose this constellation. The 
southern Fish, Piscis Australia, otherwise called Fo- 
malhaut, lies directly below the feet of Aquarius, and 
being the only conspicuous star in that part of the 
heavens, is much used in astronomical measurements. 
It is 30° south of the equator. 

About 12° east of the figure Y in the arm of Aqua- 
rius, is an assemblage of five stars, forming a pretty 
regular pentagon, which is one of the northern mem- 
bers of the Constellation Pisces ; and far to the 
northeast of this figure, north of the head of Aries, 
lies the third member, the three being represented as 



216 — 217. Describe Aquarius — Pisces. 



168 CONSTELLATIONS. 

connected together by a ribbon, or wavy band, com- 
posed of minute stars. 

CONSTELLATIONS NORTH OF THE ZODIAC. 

218. Ursa Minor (The Little Bear).— The Pole-star 
(Polaris) is in the extremity of the tail of the Little 
Bear. It is of the third magnitude, and being within 
less than a degree and a half of the North Pole of 

The Little Beak, 



7 < *>' 



""••.. "Pole Star 

the heavens, it serves, at present, to Indicate the po- 
sition of the pole. It will be recollected, however, 
that on account of the precession of the equinoxes, 
the pole of the heavens is constantly shifting its place 
from east to west, revolving about the pole of the 
ecliptic, and will in time recede so far from the pole- 
star that this will no longer retain its present distinc- 
tion. Three stars in a straight line, 4° or 5° apart, 
commencing with Polaris, lead to a trapezium of four 
stars, the whole seven together forming the figure of 
a dipper, the trapezium being the body, and the three 
first-mentioned stars being the handle. 

219. Ursa Major (The Great Bear) is one of the 



218. Describe Ursa Minor. 



NORTH OF THE ZODIAC. 169 

largest and most celebrated of the constellations. It 
is usually recognized by the figure of a larger and 
more perfect dipper than the one in the Little Bear ; 







The Gkeat Beab. 






£*- 


.* 4 


a 
f 






\ 


* 




Ms- 

y 


P 



three stars, as before, constituting the handle, and 
four others, in the form of a trapezium, the body of 
the figure. The two western stars of the trapezium, 
ranging nearly with the North Star, are called the 
Pointers ; and beginning with the northern of these 
two, and following round from left to right through 
the whole seven, they correspond in rank to the suc- 
cession of the first seven letters of the Greek alpha- 
bet — Alpha, Beta, Gamma, Delta, Epsilon, Zeta, Eta. 
Several of them also are known by their Arabic 
names. Thus, the first in the tail, corresponding to 
Epsilon, is Alioth, the next (Zeta) Mizar, and the last 
(Eta) Benetnascli. These are all bright and beautiful 
stars, -Alpha being of the first magnitude, Beta, 
Gamma, Delta, of the second, and the three forming 
the tail, of the third. But it must be remarked that 
this very remarkable figure of a dipper, or ladle, com- 
poses but a small part of the entire constellation, be- 
ing merely the hinder half of the body and the tail of 
the Bear. The head and breast of the figure, lying 



219. Describe Ursa Major. 



170 CONSTELLATIONS. 

about ten or twelve degrees west of the Pointers, con- 
tain a great number of minute stars in a triangular 
group. One of the fourth magnitude, Omicron, is in 
the mouth of the Bear. The feet of the figure may 
be looked for about 15° south of those already de- 
scribed, the two hinder paws consisting each of two 
stars very similar in appearance, and only a degree 
and a half apart. The two paws are distant from 
each other about 18°; and following westward about 
the same number of degrees, we come to another very 
similar pair of stars, which constitute one of the fore 
paws, the other foot being without any corresponding 
pair. 

In a clear winter's night, when the whole constella- 
tion is above the pole, these various parts may be 
easily recognized, and the entire figure will be seen to 
resemble a large animal, readily accounting for the 
name given to this constellation from the earliest 



220. Draco (The Dragon) is also a very large con- 
stellation) extending for a great length from east to 
west. Beginning at the tail, which lies half way be- 
tween the Pointers and the Pole-star, and winding 
round between the Great and the Little Bear, by a 
continued succession of bright stars from 5° to 10° 
asunder, it coils around under the feet of the Little 
Bear, sweeps round the pole of the ecliptic, and ter- 
minates in a trapezium formed by four conspicuous 
stars, from 30° to 35° from the North Pole. A few of 
the members of this constellation are of the second, 



220. Describe Draco. 



\ 



NORTH OF THE ZODIAC. 171 

but the greater part of the third magnitude, and be- 
low it. 

221. Cepheus (The King) is bounded north by the 
Little Bear, east by Cassiopeia, south by the Lizard, 
and west by the Dragon. The head lies in the Milky 
Way, and the feet extend toward the pole. It con- 
tains no stars above the third magnitude. 

222. Cassiopeia is bounded north and west by 
Cepheus, east by Camelopardalus, and south by An- 
dromeda, and is one of the constellations of the Milky 
Way. It is readily distinguished by the figure of a 

Cassiopeia. 

H / " J 

chair inverted, of which two stars constitute the back, 
and four, in the form of a square, the body of the 
chair. It is on the opposite side of the pole from the 
Great Bear, and nearly at the same distance from it. 

223. Camelopardalus (The Giraffe) is bounded 
north by the Little Bear, east by the head of the 
Great Bear, south by Auriga and Perseus, and west 
by Cassiopeia. Although this constellation occupies 
a large space, yet it has no conspicuous stars. 



221 — 222 — 223. Describe Cepheus — Cassiopeia — Camelopardalus. 



172 CONSTELLATIONS. 

224. Andromeda is bounded north by Cassiopeia, 
east by Perseus, south by Pegasus, and west by the 
Lizard. The direction of the figure is from south- 
west to northeast, the head coming down within 30° 
of the equator, and being recognized by a star of 
the second magnitude, which forms the northeastern 
corner of the great square in Pegasus, to be described 
hereafter. At the distance of six or seven degrees 
from the head are three conspicuous stars in a row, 
ranging from north to south, which he in the breast of 
the figure ; and about the same distance from these, 
and parallel to them, three more, which constitute the 
girdle of Andromeda. Near the northernmost of the 
three is a faint, misty object, often mistaken for a 
comet, but is a nebula, and one of the most remarka- 
ble in the heavens. 

225. Perseus is bounded north by Cassiopeia, east 
by Auriga, south by Taurus, and west by Andromeda. 
The figure extends from north to south, and is repre- 
sented by a giant holding aloft a sword in his right 
hand, while his left grasps the head of Medusa, a group 
of stars on the western side of the figure, embracing 
the celebrated star Algol. A series of bright stars 
descend along the shoulders and the waist, and there 
divide into the two legs. The western foot is 8° 
north of the Pleiades. The eastern leg is bent at the 
knee, which is distinguished by a group of small 
stars. Near the sword handle, under Cassiopeia's 
chair, is a fine cluster of stars, so close together as 
scarcely to be separable by the eye. 



224 — 225. Describe Andromeda — Perseus. 



NORTH OF THE ZODIAC. 173 

228. Auriga {Tlie Wagoner) is bounded north by 
Camelopardalus, east by the Lynx, south by Taurus, 
and west by Perseus. He is represented as bearing 
on his left shoulder the little Goat Capella, a white 
and beautiful star of the first magnitude, while Beta 
forms the right shoulder, 8° east of Capella. These 
two bright stars form, with the northern horn of the 
Bull, at the distance of 18°, an isosceles triangle. 

227. Leo Minor {The Lesser Lion) is bounded 
north by Ursa Major, east by Coma Berenices, south 
by Leo, and west by the Lynx. It lies directly under 
the hind feet of the Great Bear, and over the sickle 
in Leo, and is easily distinguished. Four stars in the 
central part of the figure, from 4° to 5° apart, form a 
pretty regular parallelogram. 

228. Canes Venatici {The Greyhounds,)- -This con- 
stellation lies between the hind legs of the Great 
Bear, on the west, and Bootes, on the east. Cor 
Caroli, a solitary star of the third magnitude, 18° 
south of Alioth, in the tail of the Great Bear, will 
serve to mark this constellation. 

229. Coma Berenices {Berenice's Hair) is a cluster 
of small stars, composing a rich group, 15° northeast 
of Denebola, in the Lion's tail, in a line between this 
star and Cor Caroli, and half way between the two. 

230. Bootes is bounded north by Draco, east by 
the Crown and the head of Serpentarius, south by 



226—227—228—229. Describe Auriga— Leo Minor— Canes Vena- 
tici — Coma Berenices. 



174: CONSTELLATIONS. 

Virgo, and west by Coma Berenices and the Hounds. 
It reaches for a great distance from north to south, 
the head being within 20° of the Dragon, and the feet 
extending to the Zodiac. In the knee of Bootes is 
Arcturus, a star of the first magnitude. The next 
brightest star, Beta, is in the head of Bootes, 23° 
north of Arcturus, and 15° east of the last star in the 
tail of the Great Bear. 



*.£ 



231, Corona Bor calls (The The Crown. 
Northern Crown) is bounded effc 
north and east by Hercules, / 
south by the head of Serpenta- 7^ f° 
rius, and west by Bootes. It \ %' Q 
is formed of a semicircle of -$£ ■ 
bright stars, six in number, of which Gamma, near 
the center of the curve, is of the second magnitude. 

232, Hercules is bounded north by Draco, east by 
Lyra, south by Ophiuchus, and west by Corona Bore- 
alis. It is a very large constellation, and contains 
some brilliant objects for the telescope, although its 
components are generally very small. The figure lies 
north and south, with the head near the head of 
Ophiuchus, and the feet under the head of Draco. 
Being between the Crown and the Lyre, its locality is 
easily determined. The eastern foot of Hercules 
forms an isosceles triangle with the two southern 
stars of the trapezium in the head of Draco ; while 
the head of Hercules is far in the south, within 15° 
of the equator, being 6° west of a similar star which 
constitutes the head of Ophiuchus. 



230 — 231 — 232. Describe Bootes — Corona Borealis — Hercules. 



NOETH OF THE ZODIAC. 175 

233. Lyra {The Lyre) is bounded north by the 
head of Draco, east by the Swan, south and west by 
Hercules. Alpha Lyrce, or Vega, is of the first mag- 
nitude. It is accompanied by a small acute triangle 
of stars. Its color is a shining white, resembling Ca- 
pella and the Eagle. 

234. Cygnus {The Swan) extends along the Milky 
Way, below Cepheus, and immediately eastward of 

The Swan. 

the Lyre, and has the figure of a large bird flying 
along the Milky Way from north to south, with out- 
stretched wings and long neck. Commencing with 
the tail, 25° east of Lyra, and following down the 
Milky Way, we pass along a line of conspicuous stars 
which form the body and neck of the figure; and 
then returning to the second of the series, we see two 
bright stars at 8° or 9° on the right and left (the three 
together ranging across the Milky Way), which form 
the wings of the Swan. This constellation is among 
the few which exhibit some resemblance to the ani- 
mals whose names they bear. 



233—234. Describe Lyra— Cygnus. 



176 CONSTELLATIONS. 

235. Vulpecula {The Little Fox) is a small constel- 
lation, in which a fox is represented as holding a 
goose in his mouth. It lies in the Milky Way, be- 
tween the Swan, on the north, and the Dolphin and 
the Arrow, on the south. 

236* Aquila {The Eagle) stretches across the Milky 
Way, and is bounded north by Sagitta, a small con- 
stellation which separates it from the Fox, east by 
the Dolphin, south by Antinous, and west by Taurus 
Poniatowski (the Polish Bull), which separates it from 
Ophiuchus. It is distinguished by three bright stars 
in the neck, known as the " three stars," which lie in 
a straight line about 2° apart, on the eastern margin 
of the Milky Way. The central star is of the first 
magnitude. Its Arabic name is Altair. 

237. Antinous lies across the equator, between the 
Eagle, on the north, and the head of Capricorn, on 
the south. 

238. Delphinns (Tlie Dolphin) is situated east and 
north of Altair, and is composed of five stars of the 
third magnitude, of which four, in the form of a 
rhombus, compose the head, and the fifth forms the 
tail. 

230. Pegasus (TJie Flying Horse) is a very large 
constellation, and is bounded north by the Lizard and 
Andromeda, east and south by Pisces, west by the 
Dolphin. The head is near the Dolphin, while the 



235—236—237—238—239. Describe Vulpecula — Aquila — Anti- 
nous — Delpliinus — Pegasus. 



SOUTH OF THE ZODIAC. 177 

back rests on Pisces, and the feet extend towards 
Andromeda. 

A large square, composed of four conspicuous mem- 
bers, one (Marhab) of the first, and three others of 
the second magnitude, distinguish this constellation. 
The corners of the square are about 15° apart, the 
northeastern corner being in the head of Andromeda. 

240. Ophiuchus is another very large constella- 
tion, the head being near the head of Hercules, and 
the feet reaching to Scorpio, the western foot being 
almost in contact with Antares. The figure is that of 
a giant holding a serpent in his hands. The head of 
the serpent is a little south of the Crown, and the tail 
reaches far eastward towards the Eagle. 

CONSTELLATIONS SOUTH OF THE ZODIAC. 

241. Cetus {The Whale) is distinguished rather for 
its extent than its brilliancy, occupying a large tract 
of the sky south of the constellations Pisces and 
Aries. The head is directly below the head of Aries, 
and the tail reaches westward 45°, being about 10° 
south of the vernal equinox. Menhir (Alpha Ceti), the 
largest of its components, is situated in the mouth, 
25° southeast of Alpha Arietis ; and Mira (Omicron 
Ceti), in the neck, 14° west -of Menkar, is celebrated 
as a variable star, which exhibits different magnitudes 
at different times. 

242. Orion is one of the most magnificent of the 
constellations, and one of those that have longest 



240—241. Describe Ophiuchus — Cetus 



178 CONSTELLATIONS. 

attracted the admiration of mankind, being alluded 
to in the Book of Job, and mentioned by Homer. 
The head of Orion lies southeast of Taurus, 15° from 
Aldebaran, and is composed of a cluster of small 
stars. Two very bright stars, Betelgeuse, of the first, 



«#■ 



Orion. 



* 
* 



7* 



ft* 



and Bellatrix, of the second magnitude, form the 
shoulders ; three more, resembling the three stars of 
the Eagle, compose the girdle ; and three smaller 
stars, in a line inclined to the girdle, form the sword. 
Bigel, of the first magnitude, makes the west foot, 
but the corresponding star, 9° southeast of this, 
which is sometimes taken for the other foot, is above 
the knee, this foot being concealed behind the Hare. 
Orion's club is marked by three stars of the fifth 
magnitude, close together, in the Milky "Way, just 
below the southern horn of the Bull. Orion is a 
favorite constellation with the practical astronomer, 



242. Describe Orion. 



SOUTH OF THE ZODIAC. 179 

abounding, as it does, in addition to the splendor of 
its components, with fine nebulse, double stars, and 
other objects of peculiar interest, when viewed with 
the telescope. It embraces 70 stars, plainly visible to 
the naked eye, including two of the first, four of the 
second, and three of the third magnitude. 

243, Lepus {TJie Hare). — Below Bigel, the western 
foot of Orion, is a small trapezium of stars, which 
forms the ears of the Hare ; and an assemblage of 
nine stars, of the third and fourth magnitudes, south 
and east of these, make up the remaining parts of 
the figure. 

244, Cants Major {The Greater Dog) lies directly 
east of the Hare, and is highly distinguished by con- 
taining Sirius, the most splendid of all the fixed 
stars, which lies in the mouth of the figure. In the 
fore paw, 6° west of Sirius, is a star of the second 
magnitude {Beta Ganis Majoris), and from 10° to 15° 
south of Sirius is a collection of stars of the second 
and third magnitude, which make up the hinder por- 
tions of the figure. The Egyptians, who anticipated 
the rising of the Nile by the appearance of Sirius in 
the morning sky, represented the constellation by the 
figure of a dog, the symbol of a faithful watchman. 

245* Canis Minor {The Lesser Dog). — About 25° 
north of Sirius is the bright star Procyon, also of the 
first magnitude, which marks the side of the Lesser 
Dog. A star of the third magnitude (Beta), 4° north- 
west of this, in the head of the figure, forms, with 



243 — 244 — 245. Describe Lepus — Canis Major — Canis Minor. 



180 CONSTELLATIONS. 

Procyon, the lower side of an elongated parallelo- 
gram, of which Castor and Pollux, 25° north, form 
the upper side. 

246. Monoceros is a large constellation, occupying 
the space between the Greater and the Lesser Dog, 
but has no conspicuous members. 

247. Hydra occupies a long space south of Leo, 
Virgo, and Libra. Its head, which is south of the 
fore paws of the Lion, consists of four stars of the 
fourth magnitude, of nearly uniform appearance ; and 
about 15° southeast of these is the Heart (Cor Hydrce), 
23° south of Eegulus. Besting on Hydra, and south 
of the hind feet of Leo, is Crater (the Cup), consist- 
ing of six stars of the fourth magnitude, arranged in 
the form of a semicircle ; and a little further east, 
also perched on the back of Hydra, is Corvus (the 
Crow), the two brightest components of which are 
situated in one of the wings of the figure, in a line 
between Crater and Spica Yirginis. 

EVENING CONSTELLATIONS OF THE DIFFERENT 

SEASONS. 

248. Since the sun passes from west to east round 
the heavens once in a year, the constellations of the 
evening sky will continually vary with the season. 
Hence one portion of the heavens can be best studied 
in the spring, another in the summer, a third in the 
autumn, and the fourth and remaining part in the 



246 — 247. Describe Monoceros — Hydra. 

248. Why do we see different constellations in the evenings of 
each season ? 



EVENING CONSTELLATIONS. 181 

winter. The following general descriptions, adapted 
to the times of the equinoxes and solstices, may 
afford some aid in these studies : 

249» Evening Constellations of Autumn* — For the 

Middle of September, from 8 to 10 d clock. — At 8 o'clock 
Scorpio is near setting in the southwest, Antares be- 
ing near 10° high. The bow of Sagittarius is on the 
eastern margin of the Milky Way, the arrow being 
directed to a point a little below Antares. At 9 
o'clock the horns of the Goat come upon the me- 
ridian ; and at 10 o'clock, the western shoulder of 
Aquarius. The other shoulder, and the figure Y in 
the a*rm, may also be easily found from the descrip- 
tion given (Art. 216) ; also, the Pentagon, in Pisces, 
and Fomalhaut (the Southern Fish), a solitary bright 
star far in the south, only 16° above the horizon. The 
head of Aries appears in the east, and the Pleiades 
are but little above the horizon, while Aldebaran is 
just rising. Keturning now to the west (at 10 o'clock), 
the Crown is seen a little north of west, about 20° 
high ; Lyra is 30° west of the zenith ; the Swan is 
nearly overhead ; and following down the Milky Way, 
the Eagle is seen on its eastern margin over against 
Lyra on the western ; and the Dolphin, a little east- 
ward of the Eagle, and as far above the horns of 
Oapricornus as the latter are above the southern 
horizon. Following on the east of the meridian, the 
great square in Pegasus may next be identified ; and 
since the northeastern corner of the square is in the 
head of Andromeda, this constellation may next be 



249. Describe the appearance in a September evening. 



182 CONSTELLATIONS. 

learned ; and then Perseus and Auriga, which appear 
still further east. Directly north of Perseus is Cas- 
siopeia's chair; and next to that we may take the 
Pole-star, the Little Bear, and the Great Bear, the 
Dipper only being traced for the present. Com- 
mencing now at the tail of the Dragon, we may trace 
round this figure, between the two Bears, to the 
head, which brings us back to Lyra and the feet of 
Hercules. 

250, Evening Constellations of Winter, — For the 

Middle of December, from 7 to 10 o clock. — Of the con- 
stellations of the Zodiac, Taurus and Gemini are now 
favorably situated for observation in the east. At 7 
o'clock the tail of Cetus just reaches the meridian, its 
head being seen below the feet of Aries. Orion is 
just risen in the southeast. At 9 o'clock, just above 
the western horizon, are seen in succession, from 
south to north, Aquarius, the Dolphin, the Eagle, the 
Lyre, and the Dragon's head. Between the Eagle 
and the Lyre, at a little higher altitude, we perceive 
the Swan, flying directly downwards. Between the 
tail of the Swan and the Pole-star is Cepheus ; and 
from the pole, along the meridian, we trace Cassio- 
peia, the feet of Andromeda, the head of Aries, and 
the neck of the Whale. At 10 o'clock Perseus has 
reached the meridian, the star Algol, in the head of 
Medusa, being directly overhead. The Pleiades are 
but little eastward of the zenith ; and following along 
south from the pole, at the interval of from one to 
two hours east of the meridian, we may trace in suc- 



250. Describe tlio appearance in a December evening. 



EVENING CONSTELLATIONS. 183 

cession, Camelopard, Auriga, Taurus, Orion, and the 
Hare. Turning along the eastern horizon, we find 
Canis Major, Monoceros, Canis Minor, the head of 
Hydra (just rising), Cancer, Leo, the sickle just ap- 
pearing about 3° north of the east point. Leo Minor 
and Ursa Major complete the survey ; and we may 
now advantageously trace out the various parts of the 
Great Bear, as described (Art. 219) ; the two stars 
composing its hindmost paw being scarcely above the 
horizon. 

251. Evening Constellations of Spring. — For the 

Middle of March, from 8 to 10 o'clock. — At 8 o'clock 
we see the Twins nearly overhead, and Procyon 
and Sirius, at different intervals, towards the south. 
Along the west we recognize the neck and head of 
the Whale, the head of Aries, and the head of An- 
dromeda ; next above these, Orion, Taurus, Perseus, 
Cassiopeia, and Cepheus ; and north of the head of 
Orion, we see Auriga and Camelopard. In the 
south, Hydra is now fully displayed ; and following 
on north, we obtain fine views of the Greater and 
the Lesser Lion, and the Great Bear. At 9 o'clock 
Crater and Corvus appear in the southeast, on the 
back of Hydra ; Yirgo extends from Leo down to the 
horizon, Spica Yirginis being about 5° high ; and 
north of Virgo, we trace in succession Coma Bere- 
nices, Cor Caroli, Bootes, with Arcturus and the 
Crown lying far in the northeast. 

252. Evening Constellations of Summer. — For the 

Middle of June, from 9 to 10 o'clock. — At 9 o'clock, 



251. Describe tlie appearance in a March evening. 



184: CONSTELLATIONS. 

Bootes, Corona Borealis, the head of Libra, the Ser- 
pent, and Scorpio, lie along on either side of the me- 
ridian. Castor and Pollux are just setting, and Leo 
is about an hour high. East of Leo, Yirgo is seen 
extending along towards the meridian, Spica being 
about 30° above the southern horizon. North of Leo 
and Yirgo, we recognize Leo Minor, Coma Berenices, 
Cor Caroli, and Ursa Major. At 10 o'clock, we trace 
along the eastern side of the meridian, Draco, Her- 
cules, and Ophiuchus ; and east of these, the Lyre, 
the Eagle, Antinous, Sagittarius, and Capricornus. 
North of the Eagle, and round to the east, we find 
Cepheus and Cassiopeia, Andromeda rising in the 
northeast, Pegasus in the east, and Aquarius in the 
southeast. 



252. Describe tlie appearance in a June evening. 



CHAPTEE XV. 

DISTANCES AND MOTIONS OF STARS — DOUBLE STAES, 
CLUSTERS, AND NEBULAE. 

253. Effect of Telescopic Power on Fixed Stars. 

One indication of the vast distance of fixed stars is, 
that no power of a telescope has ever sensibly magni- 
fied them. Even under a power which increases the 
diameter of a body 5,000 times, they appear no larger 
than to the naked eye. It is inferred that they fill 
an angle so small that 5,000 times that angle is still 
too minute to be perceived. Any appearance of dish 
which a star presents, either with a telescope or with- 
out, is the effect of the light upon the retina of the 
eye. It is called a spurious disk, since an increase of 
magnifying power causes no increase of its diameter. 

254:. Annual Parallax. — Another proof that the 
fixed stars are at an immense distance from us is the 
fact that while we shift our position every six months 
from one side of the earth's orbit to the opposite, a 
distance of 190,000,000 miles, there is no perceptible 
change in the relation of the stars to each other. It 
is only after long-continued and most accurate ob- 



253. Wiiat is the effect of the telescope on the fixed stars ? 



186 DISTANCES OF THE STAES. 

servation that a few stars have been discovered to 
suffer an annual change of position, which is clearly 
of the nature of parallax. 

The annual parallax of a star is the angle, at the 
star, subtended by the radius of the earth's orbit. 
As this angle is, in almost all cases, too small to be 
detected, it shows that the earth's orbit, seen from 
the distance of the stars, appears as a mere point. 

It is justly reckoned among the greatest achieve- 
ments in practical astronomy that the annual parallax 
has, in a few cases, not only been clearly detected as 
existing, but has been satisfactorily measured, though 
it is never so great as 1". The greatest parallax yet 
measured is that of Alpha Centauri, which is 0.91". 

The parallax of a star is most satisfactorily deter- 
mined when it is in the same telescopic field with 
other stars ; for then the distances between the stars 
may be measured with great precision by a microme- 
ter, and all errors arising from refraction and other 
disturbing causes are wholly avoided, because all the 
stars in the same field are affected alike. Parallax is 
is the only circumstance which can produce an an- 
nual change in their relative positions. The star 61 
Cygni is, in this respect, very favorably situated, and 
its parallax is thought to be quite accurately deter- 
mined. It is 0.35". 

255. Distances of the Stars. — When the parallax 
of a body is found, its distance can be computed by 
trigonometry. It is thus ascertained that Alpha Cen- 



254. What is annual parallax ? What is the greatest parallax of 
a star ? 



NATURE OF FIXED STARS. 187 

tauri, the nearest star, is about 22,000,000,000,000 
miles from us ; and 61 Cygni, the next nearest, is 
57,000,000,000,000 miles distant. Light, moving at 
the rate of 192,500 miles per second, would require 
about 3J years to come to us from Alpha Centauri, 
and 9 J years from 61 Cygni. 

As to all other stars, it is only known that they are 
still more distant. There is no improbability that, 
from the remotest telescopic stars yet seen, light may 
occupy thousands of years in coming to us. There- 
fore, we see all the stars as they were years ago ; per- 
haps not as they are now. And if at any time a 
change has been detected in the aspect or place of 
a star, that change occurred, not when it was seen, 
but 10, 100, or 1,000 years before, according to its 
distance. 

256* Nature of the Fixed Stars. — The stars are 
situated at such vast distances from the solar system 
that if they merely reflected the light of the sun, 
they would be invisible. In order to exhibit such 
brightness as they do, they must not only shed light, 
but a very intense light of their own. They cannot be 
compared with any one of the bodies in the solar sys- 
tem except the sun itself. All the fixed stars, there- 
fore, are to be considered as suns, and probably the 
centers of systems resembling the solar system. It is 



255. Which, is the nearest star ? What is its distance ? Which 
is the next nearest ? Its distance ? How long would light require 
to come from each ? What is known of other stars ? 

258. What is the nature of the stars? Why are they suns? 
Compare Alpha Centauri and Sirius with the sun. At the distance 
of the stars, how would the sun appear ? 



188 DOUBLE STAES. 

ascertained, respecting some of those stars whose dis- 
tance is known, that they shed more light than the 
sun. For example, Alpha Centanri has been found 
to shed near four times as much light as the sun ; and 
Sirius one hundred times as much. On the other hand, 
if the sun were removed from us to the nearest fixed 
star, its apparent diameter would be only T |V'> an ^» 
therefore, it would be a star having no sensible mag- 
nitude, and having only J- of the brightness of Sirius. 

257* Double Stars. — It is discovered, in a great 
number of instances, that a fixed star, when exam- 
ined by the telescope, really consists of two stars, 
very close to each other. If the distance between 
them does not exceed 32", such stars are called double 
stars. Their distance apart is often less than 1'', and 
some are so close that the highest power of the tele- 
scope and the most acute vision are requisite to sepa- 
rate them. Hence, certain double stars are habitu- 
ally used as tests of the excellence of an instrument. 

"When Sir "William Herschel first began his observa- 
tions on this class of objects, in 1780, he knew of 
only four ; but he extended the list to 500 himself, 
and the number now known exceeds 6,000. 

The two stars which compose a doable star usually 
differ from each other in magnitude, and sometimes 
in color. 

258* Ttvo Ways in ivliich Stars might- Appear 

Double. — The two stars which compose a double star 



257. What are double stars ? Speak of their discovery. What 
is their number ? How do the two members of a double star often 
differ? 



BINAEY STABS. 189 

may be supposed either to be really near each other, 
or only to appear near together, because they fall 
almost into the same line of vision, while one is actu- 
ally at an immense distance beyond the other. In 
the latter case, the stars are said to be optically 
double. "When Sir William Herschel commenced 
examining double stars, he very naturally supposed 
that, in the very few cases known, one star happened 
thus to be nearly in the same visual line with the 
other ; and he began the work of observing them 
with the expectation of detecting annual parallax in 
objects so favorably situated. For, if the nearer star 
is perceptibly affected by parallax, it would exhibit an 
annual motion relatively to the more distant star in a 
manner not to be mistaken. 

259. Binary Stars, — It soon became evident, how- 
ever, that double stars are too numerous to allow the 
supposition that they appear near to each other acci- ' 
dentally. But the question was soon set at rest by 
another most interesting discovery, namely, that some 
of the double stars exhibit motions which indicate a 
revolution of one around the other ; or, rather, of the 
two around a common center, and in periods of vari- 
ous lengths, having no connection whatever with the 
earth's annual motion. Such motion cannot be par- 
allactic ; it must be real ; and such stars are not opti- 
cally, but physically double. They are called Binary 



258. In what two ways might stars appear double ? What did 
Herschel anticipate when he first saw them ? 

259. What did he discover ? What are binary stars ? What are 
their orbits ? What law prevails among the stars ? 



190 STELLAE OEBITS. 

Stars, and are to be regarded as the centers of double 
stellar systems. 

The orbits of the binary stars are ellipses. It is 
known, therefore, that the law of gravitation outside 
of the solar system is the same as within it. 

260. Periods of Binary Stars. — The shortest pe- 
riod known is that of Zeta Herculis, about 31 years. 
The period of Eta Coronae is 43 years; that of Xi 
UrssB Majoris 58 years. These, and a few others of 
short period, have completed their revolutions once 
or twice since they were discovered. The orbits of 
such are quite accurately determined. Alpha Cen- 
tauri has not yet made a revolution since its discov- 
ery. Its period is calculated to be 77 years. A large 
number of binary stars, whose periods are computed 
to be some hundreds or thousands of years, have 
been observed as yet only through a short arc ; hence 
their periodic times, and the forms of their orbits, are 
quite uncertain. 

261. Dimensions of Stellar Orbits. — There are two 
binary stars whose parallax has been so satisfactorily 
measured that their distances from us may be consid- 
ered as well known. These are Alpha Centauri and 
61 Cygni. Hence, by the angular length of the semi- 
major axes of their orbits, we may find the mean 
radius vector of each. That of Alpha Centauri is 
about 1,500,000,000 miles, and that of 61 Cygni is 
about 4,200,000,000 miles. 



260. State the periods of some of the double stars. 

261. What orbits of double stars are known ? How large are 
they? 



TEMPORARY STARS. 191 

262. Triple and Quadruple Stars. — There are a 
few instances of three or four stars, which are known 
to be physically connected, and to constitute a sys- 
tem. Zeta Cancri is triple, and Epsilon Lyrse is 
quadruple. In each of these, the component stars 
have a slow motion about each other. 

263 o Periodic and Temporary Stars. — There are 
among the fixed stars several instances in which there 
appear to be revolutions of another sort, the nature 
of which is not understood. Stars which exhibit 
these changes are called periodic stars. A remarka- 
ble example occurs in the star Omicron Ceti. It 
passes through its changes of brightness in about 11 
months. When brightest, it is of the second magni- 
tude, and remains so for two weeks. It then dimin- 
ishes during three months to the tenth magnitude, 
remains thus five months, and increases again during 
three months to its maximum of brightness. 

Algol (Beta Persei) has a very short period, occu- 
pying only 2d. 20h. 48m. Its changes succeed each 
other with great regularity, thus : 

During 2d. 14A. Qm it remains of the second magnitude. 
" Qd. %Ji. 24m. diminishes from second to fourth. 
" Qd. Sh. 24m. increases from fourth to second. 



2d. 207i. 48m. whole period. 

iSome of this class of stars have periods of only a 
few days, while in others the changes go on very 



262. Are there any combinations more complex still ? 

263. State what is meant by periodic stars. Describe two. What 
others are probably of this class ? 



192 NEBULA. 

slowly, and appear to require several years. The 
periods of some are quite uniform, and of others 
irregular. 

To this class probably belong those stars which are 
called temporary stars. That of 1572 is celebrated. 
It appeared so suddenly, and of such brilliancy, as to 
attract the attention of common people, and rapidly 
increased, till in a few weeks it surpassed Jupiter in 
brightness. It then faded slowly, and, after about 1 J 
years, entirely disappeared. Several other cases less 
marked than this are on record. And the earlier 
catalogues contain numerous stars which are not to 
be found at the present day. 

264. Clusters of Stars.— The fixed stars are fre- 
quently grouped together in clusters; such as the 
Pleiades, in Taurus ; Presepe, in Cancer ; and Coma 
Berenices. If a telescope of low power is used, the 
number of stars appears greatly increased. 

There are others which, to the naked eye, appear 
to be nebulous, but, by the use of the telesccope, are 
plainly seen to be clusters ; and in some of them the 
stars are so numerous as not to be easily counted. 
The clusters in Perseus and Hercules are fine exam- 
ples. For the latter, see Fig. 1, frontispiece. 

285. Nehulw. — These are faint patches of light, 
having generally an ill-defined edge, and, in ordinary 
telescopes, presenting the same nebulous aspect 
which the closer clusters do to the naked eye. As 
the powers of the telescope are increased, many neb- 



264. Mention some clusters of stars. 



THE GALAXY. 193 

ulae are resolved into clusters of stars, while many 
others retain their nebulous appearance under every 
power yet employed. The number of nebulae now 
known exceeds 4,000. The forms of nebulae are vari- 
ous, and may be classified as follows *. 

1. Globular, — These appear circular in their outline, 
and generally grow brighter from the edges toward 
the center. The Planetary Nebvke have a well defined 
edge, and no bright center. The Nebulous Stars have 
only a bright point at the center, and a uniform nebu- 
losity about it. 

2. Elliptical. — A large number of the nebulae have 
this form, the most remarkable example of which is 
the great nebula of Andromeda. 

3. Spiral. — This form is becoming more frequent as 
telescopes are improved, and the more delicate fea- 
tures traced. The whirlpool nebula, near the tail of 
the Great Bear, is a fine example. See Fig. 2, 
frontispiece. 

4. Annular. — A few nebulae appear ring-like, being 
more luminous on the edges than in the center. The 
nebula of Lyra is annular. 

5. Irregular. — All the previous forms imply the 
existence of revolution in the material of which the 
nebula is composed. But there are others which are 
wholly irregular. None is more remarkable than the 
great nebula of Orion. 

268. TJie Galaxy, — This is a belt, or zone, of neb- 
ulous appearance, which encircles the heavens, nearly 



265. What are nebulae? Name the several forms. What re- 
markable ones of these forms ? 



194 THE GALAXY. 

coincident with a great circle, and cuts the plane of 
the equator afc an angle of 63°. It is usually called 
the Milky Way. Near the constellation Cygnus, it 
divides into two parts, which continue separate nearly 
a semicircle (150°), and then reunite. Its edges are 
generally ill-defined, and also quite crooked and 
irregular, having many projections and indentations. 
The telescope shows that the whiteness of the 
galaxy is due to unnumbered stars, too faint to be 
seen individually. Their distribution is quite un- 
equal ; the stars, in some parts, being crowded very 
closely together, while here and there spaces occur 
which contain but few. These inequalities are most 
marked in the southern hemisphere. In the most 
luminous parts, Sir William Herschel estimated that, 
within an area of less than T \$ part of the hemi- 
sphere, there passed the field of his telescope 50,000 
stars, large enough to be distinctly seen. The whole 
number of stars in the Milky Way is to be reckoned 
by millions. 

266. What is the galaxy? Describe its extent. What does it 
consist of? 



